Greatest Common Factor GCF

1
Greatest Common Factor GCF

• The greatest number that is a factor of 2 or more
  numbers

2
Find the GCF of

• 14, 21
• 14 1,2,7,14
• 21 1,2,3,7,21
• 1 and 7 are common factors
• 7 is the greatest common factor

3
Find the GCF of 24, 32

• 24 1,2,3,4,6,8,12,24
• 32 1,2,4,8,16,32
• 1,2,4,8, are common factors
• 8 is the GCF

4
Find the GCF of 42,72,84

• 42 1,2,3,6,7,14,21,42
• 72 1,2,3,4,6,8,9,12,18,24,36,72
• 84 1,2,3,4,6,7,12,21,42,84
• 1,2,3,6 are common factors
• 6 is the GCF

5
Relatively Prime

• 2 numbers are relatively prime if their GCF is 1

Example 56, 81 56 1,2,4,7,8,14,28,56 81
1,3,9,27,81 1 is the only common factor so 56
and 81 are relatively prime
6
Use the divisibility rules to find factors of
numbers

• Check the last digit to see it is even, ends in 5
  or 0
• Add the digits to see if 3 or 9 is a factor
• If it is even, the number that is half of it has
  factors that will also go into the number
• ex 42 1, 42, 2, 21,(so 7 and 3 will also
  go into 42, 7x6 and 3x14)

7
Find GCF using Prime Factors

• 90 2 x 3 x 3 x 5
• 150 2 x 3 x 5 x 5
• multiply common factors
• 2 x 3 x 5 30

8

• 84 2 x 2 x 3 x 7
• 216 2 x 2 x 2 x 3 x 3 x 3
• multiply the common factors
• 2 x 2 x 3 12 GCF

9
If the GCF is 1, then they are relatively prime

• 36 2 x 2 x 3 x 3
• 91 7 x 13
• there are no prime factors in common, so
  their GCF is 1

10
Finding the GCF of 3 numbers

• 63 3 x 3 x 7
• 84 2 x 2 x 3 x 7
• 126 2 x 3 x 3 x 7
• multiply common factors of all 3
• 3 x 7 21