Factors (or divisors) of a number n are all integers that divide n exactly with no remainder. Prime factorization expresses n as a product of prime numbers — unique for every integer greater than 1 (Fundamental Theorem of Arithmetic).
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Pro Tip
To find all factors: find the prime factorization first. For 12 = 2²×3: factors are 2⁰×3⁰=1, 2¹×3⁰=2, 2²×3⁰=4, 2⁰×3¹=3, 2¹×3¹=6, 2²×3¹=12. Systematic and complete.
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Did You Know?
Perfect numbers equal the sum of their proper divisors: 6 = 1+2+3, 28 = 1+2+4+7+14. Only 51 perfect numbers are known. All known ones are even; whether any odd perfect numbers exist is one of the oldest unsolved problems in mathematics.
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