Write the numbers in their prime factorisations. the GCF is the product of the common primes (each time they appear).
Example: 30 and 42
2 x 3 x 5 = 30
2 x 3 x 7 = 42
Select the common factors.
2 x 3 = 6, the GCF
Example: 24 and 60
24 = 2 × 2 × 2 × 3
60 = 2 × 2 × 3 × 5
GCF = 2 × 2 × 3 = 12
The prime 2 appears twice in both numbers.
If you use the power format of the prime factorisation, the GCF is the product of each of the common primes to the LOWEST power across the numbers.
For 24 and 60 this gives:
24 = 2³ × 3
60 = 2² × 3 × 5
→ GCF = 2² × 3 = 12
As the lowest power of 2 across the numbers is 2²,
the lowest power of 3 across the numbers is 3 = 3¹,
5 is not common, but for completeness, 24 = 2³ × 3¹ × 5⁰ since 5⁰ = 1, so the lowest power of the prime 5 across the numbers is 5⁰:
→ GCF = 2² × 3¹ × 5⁰ = 4 × 3 × 1 = 12.
The prime factorization of 9 is 32 You need at least two numbers to find a GCF.
You need at least two numbers to find a GCF. The prime factorization of 207 is 3 x 3 x 23.
Once your prime factorization is complete and you discover that there are no numbers in common, the GCF is one and the numbers are declared to be relatively prime.
Use the prime factorizations to determine the GCF. If the GCF is 1, the numbers are relatively prime. If the two numbers have no prime factors in common, they are relatively prime.
The prime factorization of 124 is 2 * 2 * 31 = 22 * 31. The prime factorization of 24 is 2 * 2 * 2 * 3 = 23 * 3. The GCF contains all prime factors contained in both numbers. We find 22 is in both, so the GCF is 4.
The prime factorization of 9 is 32 You need at least two numbers to find a GCF.
You need at least two numbers to find a GCF. The prime factorization of 207 is 3 x 3 x 23.
At least two or more numbers are needed to find their GCF
Whatever you use, you need at least two numbers to find a GCF.
You can find the GCF and/or the LCM of a set of numbers by comparing the prime factorizations of the individual members of the set.
Prime factorization of 32 = 2x2x2x2x2 Prime factorization of 90 = 2x3x3x5 Prime factorization of 30 = 2x3x5 What is common in the prime factorization of the numbers? Only 2 is common, so GCF is 2.
You need at least two numbers to find a GCF, whichever method you use.
Prime factorization for 135 = 3 x 3 x 3 x 5Prime factorization for 351 = 3 x 3 x 3 x 13GCF of (135,351) = 27
You need at least two numbers to find a GCF.
You need at least two numbers to find a GCF.
You need at least two numbers to find a GCF.
You need at least two numbers to find a GCF.