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 PRACTICE:     ("Click" on Check answer or use the answer key below.) 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 Amby's Math Instruction, Reinforcement, and Learning Activities Math Education Resources Math Puzzles & Learning Activities Directory Brain Games Cat Site Education Internet Mensa Portfolios Test Prep Work Site © 1999 Amby Duncan-Carr   All rights reserved. The URL of this page is: http://amby.com/educate/math/2-1_GCF.html