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:<math>24 = 2^3 * 3</math>.
:<math>24 = 2^3 * 3</math>.
The Prime Factorisation Theorem guarantees that every integer has one unique prime factorization, e.g. 24 =2<sup>3</sup>3<sup>1</sup>, though it may have multiple non-prime factorizations (e.g. 24 = 2 * 12, 6 * 4, 3 * 8).
The Prime Factorisation Theorem guarantees that every integer has a unique prime factorization, e.g. 24 =2<sup>3</sup>3<sup>1</sup>, though it may have multiple non-prime factorizations (e.g. 24 = 2 * 12, 6 * 4, 3 * 8).
The number of divisors of an integer may be determined from its prime factorization when expressed in exponent form, by incrementing each exponent by 1 and multiplying the results. In the example above, the exponents of prime factors 2 and 3 are 3 and 1, respectively. The number of divisors of 24 is therefore
The number of divisors of an integer may be determined from its prime factorization when expressed in exponent form, by incrementing each exponent by 1 and multiplying the results. In the example above, the exponents of prime factors 2 and 3 are 3 and 1, respectively. The number of divisors of 24 is therefore