5, 10
10, 15
5, 15
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The only factor that all of these numbers share is 1 since 3 and 5 are prime. So 1 is the gcf of this set of numbers.
The GCF is 5.
15*3 = 3*5*3 = 3*3*5 18*5 = 2*3*3*5 = 2*3*3*5 So GCF = numbers that appear in both lists (however many times in both) = 3*3*5 = 45
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.
5 and any multiple of 5 5,10 5,15 5,20