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Find the prime factorization of 72.

April 10, 2026Mathematics

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Answer

2^3 \times 3^2

3 steps

Find the prime factors of 72.
Divide 72 by the smallest prime number, 2.
$72 \div 2 = 36$
Divide 36 by 2.
$36 \div 2 = 18$
Divide 18 by 2.
$18 \div 2 = 9$
Now, 9 is not divisible by 2. Divide 9 by the next smallest prime number, 3.
$9 \div 3 = 3$
Divide 3 by 3.
$3 \div 3 = 1$
The prime factors of 72 are $2, 2, 2, 3, 3$ .
Write the prime factorization using exponents.
Count the occurrences of each prime factor:
The prime factor 2 appears 3 times, so it can be written as $2^3$ .
The prime factor 3 appears 2 times, so it can be written as $3^2$ .
Combine the exponential forms to get the prime factorization of 72.
$72 = 2 \times 2 \times 2 \times 3 \times 3 = 2^3 \times 3^2$
The prime factorization of 72 is $\boxed{2^3 \times 3^2}$ .

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