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What is the greatest common factor (GCF) of 105 and 175?

May 20, 2026Mathematics

ScanSolve AI Answer

Answer

35

4 steps

To find the greatest common factor (GCF) of two numbers, we can use their prime factorization.

Find the prime factorization of 105.
$105 = 3 \times 35 = 3 \times 5 \times 7$
Find the prime factorization of 175.
$175 = 5 \times 35 = 5 \times 5 \times 7 = 5^2 \times 7$
Identify the common prime factors and their lowest powers.
The common prime factors are 5 and 7.
The lowest power of 5 is $5^1$ .
The lowest power of 7 is $7^1$ .
Multiply the common prime factors raised to their lowest powers to find the GCF.
$\text{GCF} = 5 \times 7 = 35$
The GCF is 35.

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