Here is the complete solution to the
GCF of Monomials - WS-2-MCQ worksheet.
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🔍 How to Find GCF of Monomials:
To find the
Greatest Common Factor (GCF) of two monomials:
1.
Find the GCF of the coefficients (numerical parts) — use prime factorization or listing factors.
2.
For each variable, take the
lowest exponent that appears in both monomials.
3. Multiply the GCF of coefficients and the common variables with their lowest exponents.
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##
✔ Solutions:
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1) `18a², 36`
- Coefficients: GCF(18, 36) =
18
- Variables: Only first has `a²`, second has no `a` →
no common variable
-
✔ Answer: A) 18
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2) `42yx², 28x⁴`
- Coefficients: GCF(42, 28) =
14
- Variables:
- `y`: only in first → skip
- `x`: min exponent = min(2, 4) =
x²
- So GCF =
14x²
-
✔ Answer: A) 14x²
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3) `36xy, 25`
- Coefficients: GCF(36, 25) =
1 (coprime)
- Variables: 25 has none → no common variable
-
✔ Answer: B) 1
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4) `22, 33a²`
- Coefficients: GCF(22, 33) =
11
- Variables: 22 has none → no common variable
-
✔ Answer: B) 11
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5) `14n², 21`
- Coefficients: GCF(14, 21) =
7
- Variables: 21 has no `n` → no common variable
-
✔ Answer: B) 7
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6) `35x, 10xy`
- Coefficients: GCF(35, 10) =
5
- Variables:
- `x`: min exponent = min(1,1) =
x
- `y`: only in second → skip
- GCF =
5x
-
✔ Answer: C) 5x
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7) `42, 30xy`
- Coefficients: GCF(42, 30) =
6
- Variables: 42 has none → no common variable
-
✔ Answer: D) 6
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8) `27m, 27m³`
- Coefficients: GCF(27, 27) =
27
- Variables: `m` → min exponent = min(1,3) =
m
- GCF =
27m
-
✔ Answer: A) 27m
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9) `30x³, 40x⁴`
- Coefficients: GCF(30, 40) =
10
- Variables: `x` → min exponent = min(3,4) =
x³
- GCF =
10x³
-
✔ Answer: A) 10x³
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10) `32x, 3`
- Coefficients: GCF(32, 3) =
1
- Variables: 3 has none → no common variable
-
✔ Answer: D) 1
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11) `21, 28x`
- Coefficients: GCF(21, 28) =
7
- Variables: 21 has none → no common variable
-
✔ Answer: D) 7
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12) `27y², 36x²y`
- Coefficients: GCF(27, 36) =
9
- Variables:
- `x`: only in second → skip
- `y`: min exponent = min(2,1) =
y
- GCF =
9y
-
✔ Answer: D) 9y
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13) `6u²v², 6v²`
- Coefficients: GCF(6,6) =
6
- Variables:
- `u`: only in first → skip
- `v`: min exponent = min(2,2) =
v²
- GCF =
6v²
-
✔ Answer: A) 6v²
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14) `15y, 30xy²`
- Coefficients: GCF(15, 30) =
15
- Variables:
- `x`: only in second → skip
- `y`: min exponent = min(1,2) =
y
- GCF =
15y
-
✔ Answer: A) 15y
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15) `21uv², 21v³`
- Coefficients: GCF(21,21) =
21
- Variables:
- `u`: only in first → skip
- `v`: min exponent = min(2,3) =
v²
- GCF =
21v²
-
✔ Answer: B) 21v²
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16) `21x²y, 21y³x`
- Coefficients: GCF(21,21) =
21
- Variables:
- `x`: min exponent = min(2,1) =
x
- `y`: min exponent = min(1,3) =
y
- GCF =
21xy
-
✔ Answer: C) 21xy
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## 📝 Final Answer Key:
| Question | Answer |
|----------|--------|
| 1 | A |
| 2 | A |
| 3 | B |
| 4 | B |
| 5 | B |
| 6 | C |
| 7 | D |
| 8 | A |
| 9 | A |
| 10 | D |
| 11 | D |
| 12 | D |
| 13 | A |
| 14 | A |
| 15 | B |
| 16 | C |
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✔ You’re all set! Let me know if you want a printable version or explanations for specific problems.
Parent Tip: Review the logic above to help your child master the concept of gcf monomials worksheet.
