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Find the GCF of 40 and 120.

May 25, 2026Mathematics

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Answer

\mathbf{40}

4 steps

here's how to find the GCF of 40 and 120.

Find the prime factorization of 40.
$40 = 2 \times 20 = 2 \times 2 \times 10 = 2 \times 2 \times 2 \times 5 = 2^3 \times 5^1$
Find the prime factorization of 120.
$120 = 2 \times 60 = 2 \times 2 \times 30 = 2 \times 2 \times 2 \times 15 = 2 \times 2 \times 2 \times 3 \times 5 = 2^3 \times 3^1 \times 5^1$
Identify the common prime factors and their lowest powers.
Both numbers share the prime factors 2 and 5.
The lowest power of 2 common to both is $2^3$ .
The lowest power of 5 common to both is $5^1$ .
The prime factor 3 is not common to both.
Multiply the common prime factors with their lowest powers.
$\text{GCF}(40, 120) = 2^3 \times 5^1 = 8 \times 5 = 40$
The GCF of 40 and 120 is:
$\mathbf{40}$

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