G.C.F of Monomials worksheet with 18 practice problems and an example.

To solve this worksheet, we need to find the Greatest Common Factor (G.C.F.) of each pair of monomials.

> What is G.C.F. for Monomials?
>
> The G.C.F. of two or more monomials is the product of:
> - The greatest common numerical factor (if any numbers are present — in this case, all are variables only, so we ignore coefficients),
> - And the lowest power of each variable that appears in all the monomials.

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Let’s go through each problem one by one.

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1. G.C.F of x²y and xy

- Variables: both have `x` and `y`
- Lowest power of `x`: min(2, 1) = x¹
- Lowest power of `y`: min(1, 1) = y¹
✔ Answer: xy

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2. G.C.F of ab² and ba

Note: `ba` is same as `ab`

So: `ab²` and `ab`

- Both have `a` and `b`
- Lowest power of `a`: min(1,1) = a
- Lowest power of `b`: min(2,1) = b
✔ Answer: ab

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3. G.C.F of por and rot

Variables:
- `por` → p, o, r
- `rot` → r, o, t

Common variables: o, r

Lowest powers: both have exponent 1 for o and r
✔ Answer: or

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4. G.C.F of xy and y²

- Common variable: `y`
- `x` is not in second term → exclude
- Lowest power of `y`: min(1,2) = y
✔ Answer: y

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5. G.C.F of my and ny

Common variable: `y`
`m` and `n` are different → exclude
✔ Answer: y

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6. G.C.F of abc and bc

Common variables: `b`, `c`
`a` not in second → exclude
✔ Answer: bc

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7. G.C.F of xyz² and yz

Common variables: `y`, `z`
`x` not in second → exclude
Lowest power of `y`: 1
Lowest power of `z`: min(2,1) = z
✔ Answer: yz

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8. G.C.F of abc² and bac

Note: `bac` = `abc` (commutative property)

So: `abc²` and `abc`

Common: `a`, `b`, `c`
Lowest power of `c`: min(2,1) = c
✔ Answer: abc

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9. G.C.F of m²no and mn

Common variables: `m`, `n`
`o` not in second → exclude
Lowest power of `m`: min(2,1) = m
✔ Answer: mn

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10. G.C.F of x²y and xy²

Common: `x`, `y`
Lowest power of `x`: min(2,1) = x
Lowest power of `y`: min(1,2) = y
✔ Answer: xy

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11. G.C.F of ab² and b²a

Same as `ab²` and `ab²` → identical!
✔ Answer: ab²

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12. G.C.F of por and rot

This is a repeat of #3
✔ Answer: or

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13. G.C.F of my and my

Identical monomials
✔ Answer: my

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14. G.C.F of ny and n²y

Common: `n`, `y`
Lowest power of `n`: min(1,2) = n
✔ Answer: ny

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15. G.C.F of ab²c² and bc

Common variables: `b`, `c`
`a` not in second → exclude
Lowest power of `b`: min(2,1) = b
Lowest power of `c`: min(2,1) = c
✔ Answer: bc

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16. G.C.F of yz and y²z

Common: `y`, `z`
Lowest power of `y`: min(1,2) = y
✔ Answer: yz

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17. G.C.F of ab²c and bac²

Note: `bac²` = `ab c²`

So: `ab²c` and `abc²`

Common: `a`, `b`, `c`
Lowest power of `b`: min(2,1) = b
Lowest power of `c`: min(1,2) = c
✔ Answer: abc

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18. G.C.F of n²o and n²

Common variable: `n`
`o` not in second → exclude
Lowest power of `n`: min(2,2) = n²
✔ Answer: n²

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## ✔ Final Answers:

1. xy
2. ab
3. or
4. y
5. y
6. bc
7. yz
8. abc
9. mn
10. xy
11. ab²
12. or
13. my
14. ny
15. bc
16. yz
17. abc
18. n²

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💡 Tip: Always look for variables that appear in ALL terms, then take the smallest exponent for each. Ignore variables that don’t appear in every term.

Let me know if you want a printable version or explanation with diagrams!