Find the prime factorization of 80.
A2 times 2 times 2 times 5 times 5
B2 times 2 times 2 times 2 times 3
C2 times 2 times 2 times 2 times 5
D2 times 2 times 5 times 5
Answer & Solution
Correct answer: C. 2 times 2 times 2 times 2 times 5
1. Split 80 into two factors, such as 8 and 10, and keep splitting anything that is not prime.
2. Splitting 8 gives 2, 2, and 2, and splitting 10 gives 2 and 5.
3. Every branch now ends in a circled prime: four 2s and one 5.
4. Multiply to verify: 2 times 2 times 2 times 2 is 16, and 16 times 5 is 80.
5. The option ending in times 3 multiplies to 48, and the two options with double 5s give 200 and 100, so none of them rebuild 80.
_Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 1 "Foundations", section 1.1 Introduction to Whole Numbers_
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