Greatest Common Factors

The Greatest Common Factor (G.C.F.) of two numbers is the largest number that is a divisor of both. It is sometimes called the Greatest Common Divisor. It can be used to simplify (or reduce) fractions. Don't let the "greatest" in the name fool you - the GCF is no larger than the smallest of the numbers.

HINTS:
GREATEST is biggest or largest.

COMMON is something shared or in common.

FACTORS are the parts of multiplication facts.

EXAMPLE:
Find the Greatest Common Factor (G.C.F.) of 6 and 10.

6 = 2 * 3 You can divide 6 by 2 or by 3

6 = 1 * 6 You can divide 6 by 1 or by 6

Therefore 1, 2, 3, and 6 are all factors of six.

10 = 2 * 5 You can divide 10 by 2 or by 5

10 = 1 * 10 You can divide 10 by 1 or by 10

Therefore 1, 2, 5, and 10 are all factors of ten.

Both 6 and 10 can be divided by 1 and by 2; 2 is greater than 1, so 2 is the Greatest Common Factor (G.C.F.) of 6 and 10.

You can also use the prime factorization method to find the Greatest Common Factor:

EXAMPLE:
Find the Greatest Common Factor (G.C.F.) of 36 and 54.

36 = 2 * 2 * 3 * 3

54 = 2 * 3 * 3 * 3

Both have 2 * 3 * 3 in common:

Usually you can find the Greatest Common Factor fairly easily by experimenting with possible divisors:

Start with the smaller number; it is the largest divisor of itself.
Is it a divisor of the larger number? If so, you have the G.C.F.; if not:
What is the next-largest divisor of the smaller number; is IT a divisor of the other number?
Continue until you find a number that will divide into BOTH. Sometimes only the number '1' will work as a common divisor; for example: 21 and 16 have no common factor other than 1.

EXAMPLE:
Find the Greatest Common Factor (G.C.F.) of 10 and 30.
 Will 10 go into 30? Yes: G.C.F. = 10

Find the Greatest Common Factor (G.C.F.) of 24 and 18.
 Will 18 go into 24? No. Next pair: 2 * 9 = 18 Will 9 go into 24? No. Next pair: 3 * 6 = 18 Will 6 go into 24? Yes: G.C.F. = 6

 1) What is the greatest common factor (G.C.F.) of 12 and 10. A) 1 B) 2 C) 4 D) 5 E) 6 Check answer B) 2 2)   What is the greatest common factor (G.C.F.) of 20 and 30? A) 1 B) 2 C) 4 D) 5 E) 10 Check answer E) 10 3)   What is the greatest common factor of 8 and 40? A) 1 B) 2 C) 4 D) 8 E) 10 Check answer D) 8 4)   4) What is the greatest common factor of 27 and 12? A) 1 B) 2 C) 3 D) 6 E) 9 Check answer C) 3 5)   Find the greatest common factor (G.C.F.) of 8 and 27. A) 1 B) 2 C) 3 D) 4 E) 8 Check answer A) 1 6)   Find the greatest common factor (G.C.F.) of 40 and 60. A) 1 B) 2 C) 4 D) 10 E) 20 Check answer E) 20 7)   Find the greatest common factor (G.C.F.) of 48 and 36. A) 1 B) 4 C) 6 D) 12 E) 18 Check answer D) 12 8)   Find the greatest common divisor (G.C.F.) of 18 and 8. A) 1 B) 2 C) 4 D) 6 E) 8 Check answer B) 2

ANSWERS: 1 -B     2 -E     3 -D     4 -C     5 -A     6 -E     7 -D     8 -B