# Greatest Common Factor

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## Common Factors and Divisors at eTutorWorld

**How do you factor with the greatest common factor? **

The greatest common factor is the greatest whole number that is a factor of each of two or more numbers.

There is no difference between highest common factor **(H.C.F)** and greatest common divisor **(G.C.D).**

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#### What is the greatest common factor of 9 and 12?

List the Prime factors of each number.

Prime Factors of 9: **3× 3**

Prime Factors of 12: **3×2×2**

There is one 3 in common.

The greatest common factor of 9 and 12 is 3.

List the Prime factors of each number.

Prime Factors of 18: **2 ×3× 3**

Prime Factors of 24: **2×3×2×2**

There is 2× 3 in common.

The greatest common factor of 18 and 24 is 6.

## Check Point

- Find the greatest common divisor
**(G.C.D)**of 70, 215 and 310? - What is the greatest common factor
**(G.C.F)**of 24 and 88? - Clinton is making trail mix out of 14 bags of nuts and 16 bags of dried fruit. He wants each new portion of trail mix to be identical, containing the same combination of bags of nuts bags of dried fruit, with no bags left over. What is the greatest number of portions of trial mix Clinton can make?
- Colton is making emergency preparedness kits to share with friends. She has 25 bottles of water and 35 cans of food, which she would like to distribute equally among the kits, with nothing left over. What is the greatest number of kits Veronica can make?
- Mrs. Kelly, the geography teacher, collected 36 sedimentary rocks and 92 metamorphic ones. Now she wants to create some identical kits for studying rocks, without having any rocks left over. What is the greatest number of kits she can create?

##### Answer key

- G.C.F=5
- G.C.D=8
- The greatest number of trial mix that Clinton can make is 2.
- 5 kits
- 4 kits

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