GCF of Monomials worksheet for algebra practice.
Worksheet titled "GCF of Monomials-WS-1" from Learners Planet, featuring 30 problems to find the greatest common factor of given monomials.
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Step-by-step solution for: GCF-of-Monomials-Workbook-1
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Show Answer Key & Explanations
Step-by-step solution for: GCF-of-Monomials-Workbook-1
Sure! Let’s solve each problem step by step. The task is to find the Greatest Common Factor (GCF) of each pair (or set) of monomials.
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The GCF of monomials is found by:
1. Taking the GCF of the coefficients (numerical parts).
2. Taking the lowest power of each common variable present in all terms.
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Let’s go one by one:
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- Coefficients: GCF(27, 12) = 3
- Variables: both have x¹ → lowest power = x
✔ GCF = 3x
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- Coefficients: GCF(50, 50) = 50
- Variables: only second has ‘m’ → no common variable
✔ GCF = 50
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- Coefficients: GCF(18, 45) = 9
- Variables: both have x² → lowest power = x²; first has y, second doesn’t → ignore y
✔ GCF = 9x²
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- Coefficients: GCF(28, 42) = 14
- Variables: both have m³ and n¹ → take m³n
✔ GCF = 14m³n
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- Coefficients: GCF(36, 48) = 12
- Variables: both have y¹ (lowest), x¹ → so yx
✔ GCF = 12yx
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- Coefficients: GCF(30, 35) = 5
- Variables: both have y²
✔ GCF = 5y²
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- Coefficients: GCF(48, 24) = 24
- Variables: both have y² (lowest), x only in second → ignore x
✔ GCF = 24y²
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- Coefficients: GCF(36, 48) = 12
- Variables: u¹ (lowest), v¹ → so uv
✔ GCF = 12uv
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- Coefficients: GCF(23, 48) = 1 (23 is prime)
- Variables: no common variables
✔ GCF = 1
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- Coefficients: GCF(22, 44) = 22
- Variables: u², v¹ (lowest)
✔ GCF = 22u²v
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- Coefficients: GCF(25, 50) = 25
- Variables: only first has x → no common variable
✔ GCF = 25
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- Coefficients: GCF(24, 48) = 24
- Variables: a² common; b only in first → ignore b
✔ GCF = 24a²
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- Coefficients: GCF(24, 48) = 24
- Variables: x² (lowest); y only in first → ignore y
✔ GCF = 24x²
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- Coefficients: GCF(40, 48) = 8
- Variables: none common (first has no variables)
✔ GCF = 8
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- Coefficients: GCF(44, 33) = 11
- Variables: none common
✔ GCF = 11
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- Coefficients: GCF(25, 10) = 5
- Variables: m²
✔ GCF = 5m²
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- Coefficients: GCF(42, 42) = 42
- Variables: x¹, y¹ (lowest powers)
✔ GCF = 42xy
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- Coefficients: GCF(36, 33) = 3
- Variables: no common variables (m vs n)
✔ GCF = 3
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- Coefficients: GCF(6, 18) = 6
- Variables: x¹ (lowest); y only in second → ignore y
✔ GCF = 6x
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- Coefficients: GCF(22, 44) = 22
- Variables: y¹, x²
✔ GCF = 22yx²
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- Coefficients: GCF(49, 35, 42)
- 49 = 7×7
- 35 = 5×7
- 42 = 6×7 → GCF = 7
- Variables: x¹ (lowest)
✔ GCF = 7x
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- Coefficients: GCF(27, 24, 48)
- 27=3³, 24=2³×3, 48=2⁴×3 → GCF = 3
- Variables: y¹ (common in all); x only in last two → ignore x
✔ GCF = 3y
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- Coefficients: GCF(27, 42, 12)
- 27=3³, 42=2×3×7, 12=2²×3 → GCF = 3
- Variables: y¹ (lowest)
✔ GCF = 3y
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- Coefficients: GCF(33, 44, 33) = 11
- Variables: v² (lowest common power)
✔ GCF = 11v²
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- Coefficients: GCF(20, 30, 40) = 10
- Variables: u²
✔ GCF = 10u²
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- Coefficients: GCF(18, 27, 45) = 9
- Variables: y² (lowest common)
✔ GCF = 9y²
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- Coefficients: GCF(42, 42, 21) = 21
- Variables: a¹, b¹
✔ GCF = 21ab
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- Coefficients: GCF(36, 18, 18) = 18
- Variables: x² (lowest), y only in last two → ignore y
✔ GCF = 18x²
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- Coefficients: GCF(27, 15, 45) = 3
- Variables: no variable common to all three
✔ GCF = 3
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- Coefficients: GCF(15, 50, 15) = 5
- Variables: no common variable across all
✔ GCF = 5
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## ✔ Final Answers:
1) 3x
2) 50
3) 9x²
4) 14m³n
5) 12yx
6) 5y²
7) 24y²
8) 12uv
9) 1
10) 22u²v
11) 25
12) 24a²
13) 24x²
14) 8
15) 11
16) 5m²
17) 42xy
18) 3
19) 6x
20) 22yx²
21) 7x
22) 3y
23) 3y
24) 11v²
25) 10u²
26) 9y²
27) 21ab
28) 18x²
29) 3
30) 5
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Let me know if you’d like a printable version or explanations for specific ones! 😊
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📌 What is GCF of Monomials?
The GCF of monomials is found by:
1. Taking the GCF of the coefficients (numerical parts).
2. Taking the lowest power of each common variable present in all terms.
---
Let’s go one by one:
---
1) 27x, 12x
- Coefficients: GCF(27, 12) = 3
- Variables: both have x¹ → lowest power = x
✔ GCF = 3x
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2) 50, 50m
- Coefficients: GCF(50, 50) = 50
- Variables: only second has ‘m’ → no common variable
✔ GCF = 50
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3) 18yx², 45x²
- Coefficients: GCF(18, 45) = 9
- Variables: both have x² → lowest power = x²; first has y, second doesn’t → ignore y
✔ GCF = 9x²
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4) 28m³n, 42m³n
- Coefficients: GCF(28, 42) = 14
- Variables: both have m³ and n¹ → take m³n
✔ GCF = 14m³n
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5) 36yx, 48y²x
- Coefficients: GCF(36, 48) = 12
- Variables: both have y¹ (lowest), x¹ → so yx
✔ GCF = 12yx
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6) 30y², 35y²
- Coefficients: GCF(30, 35) = 5
- Variables: both have y²
✔ GCF = 5y²
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7) 48y³, 24xy²
- Coefficients: GCF(48, 24) = 24
- Variables: both have y² (lowest), x only in second → ignore x
✔ GCF = 24y²
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8) 36uv, 48u³v
- Coefficients: GCF(36, 48) = 12
- Variables: u¹ (lowest), v¹ → so uv
✔ GCF = 12uv
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9) 23y, 48x²
- Coefficients: GCF(23, 48) = 1 (23 is prime)
- Variables: no common variables
✔ GCF = 1
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10) 22u²v, 44u²v²
- Coefficients: GCF(22, 44) = 22
- Variables: u², v¹ (lowest)
✔ GCF = 22u²v
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11) 25x, 50
- Coefficients: GCF(25, 50) = 25
- Variables: only first has x → no common variable
✔ GCF = 25
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12) 24ba², 48a²
- Coefficients: GCF(24, 48) = 24
- Variables: a² common; b only in first → ignore b
✔ GCF = 24a²
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13) 24yx², 48x⁴
- Coefficients: GCF(24, 48) = 24
- Variables: x² (lowest); y only in first → ignore y
✔ GCF = 24x²
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14) 40, 48ab
- Coefficients: GCF(40, 48) = 8
- Variables: none common (first has no variables)
✔ GCF = 8
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15) 44, 33x
- Coefficients: GCF(44, 33) = 11
- Variables: none common
✔ GCF = 11
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16) 25m², 10m²
- Coefficients: GCF(25, 10) = 5
- Variables: m²
✔ GCF = 5m²
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17) 42x²y², 42xy
- Coefficients: GCF(42, 42) = 42
- Variables: x¹, y¹ (lowest powers)
✔ GCF = 42xy
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18) 36m², 33n
- Coefficients: GCF(36, 33) = 3
- Variables: no common variables (m vs n)
✔ GCF = 3
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19) 6x², 18y²x
- Coefficients: GCF(6, 18) = 6
- Variables: x¹ (lowest); y only in second → ignore y
✔ GCF = 6x
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20) 22yx², 44yx²
- Coefficients: GCF(22, 44) = 22
- Variables: y¹, x²
✔ GCF = 22yx²
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21) 49x, 35x², 42x²
- Coefficients: GCF(49, 35, 42)
- 49 = 7×7
- 35 = 5×7
- 42 = 6×7 → GCF = 7
- Variables: x¹ (lowest)
✔ GCF = 7x
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22) 27y², 24xy, 48x²y
- Coefficients: GCF(27, 24, 48)
- 27=3³, 24=2³×3, 48=2⁴×3 → GCF = 3
- Variables: y¹ (common in all); x only in last two → ignore x
✔ GCF = 3y
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23) 27y, 42y³, 12y
- Coefficients: GCF(27, 42, 12)
- 27=3³, 42=2×3×7, 12=2²×3 → GCF = 3
- Variables: y¹ (lowest)
✔ GCF = 3y
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24) 33u²v², 44v³, 33v⁴
- Coefficients: GCF(33, 44, 33) = 11
- Variables: v² (lowest common power)
✔ GCF = 11v²
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25) 20u², 30u², 40u²
- Coefficients: GCF(20, 30, 40) = 10
- Variables: u²
✔ GCF = 10u²
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26) 18xy², 27y³, 45y²
- Coefficients: GCF(18, 27, 45) = 9
- Variables: y² (lowest common)
✔ GCF = 9y²
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27) 42ab, 42a²b², 21ab
- Coefficients: GCF(42, 42, 21) = 21
- Variables: a¹, b¹
✔ GCF = 21ab
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28) 36x³, 18yx², 18x³y
- Coefficients: GCF(36, 18, 18) = 18
- Variables: x² (lowest), y only in last two → ignore y
✔ GCF = 18x²
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29) 27b, 15ab, 45a
- Coefficients: GCF(27, 15, 45) = 3
- Variables: no variable common to all three
✔ GCF = 3
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30) 15y, 50, 15x²
- Coefficients: GCF(15, 50, 15) = 5
- Variables: no common variable across all
✔ GCF = 5
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## ✔ Final Answers:
1) 3x
2) 50
3) 9x²
4) 14m³n
5) 12yx
6) 5y²
7) 24y²
8) 12uv
9) 1
10) 22u²v
11) 25
12) 24a²
13) 24x²
14) 8
15) 11
16) 5m²
17) 42xy
18) 3
19) 6x
20) 22yx²
21) 7x
22) 3y
23) 3y
24) 11v²
25) 10u²
26) 9y²
27) 21ab
28) 18x²
29) 3
30) 5
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Let me know if you’d like a printable version or explanations for specific ones! 😊
Parent Tip: Review the logic above to help your child master the concept of gcf monomials worksheet.
