Prime Factorization in Exponent (Canonical) Form Explained (2026)

Exponent (canonical) form writes a prime factorization with each distinct prime raised to a power, like 360 = 2³ × 3² × 5. It is compact, standard, and unlocks fast formulas for divisors, the GCF and the LCM.

From expanded to canonical form

Expanded: 360 = 2 × 2 × 2 × 3 × 3 × 5. Canonical: 2³ × 3² × 5. Just count how many times each prime appears and use it as the exponent. Get either form from the Prime Factorization Calculator.

Counting divisors instantly

Add 1 to each exponent and multiply. For 360 = 2³ × 3² × 5¹, the divisor count is (3+1)(2+1)(1+1) = 24 divisors — no listing required.

GCF and LCM from exponents

For two numbers in canonical form, the GCF takes the lowest exponent of each shared prime and the LCM takes the highest. This is the cleanest way to compute both — see the GCD / GCF Calculator and LCM Calculator.

Worked example: 360

360 = 2³ × 3² × 5. Divisors: 24. With 84 = 2² × 3 × 7: GCF = 2² × 3 = 12; LCM = 2³ × 3² × 5 × 7 = 2520.

Common pitfalls

Do not forget the implicit exponent of 1, and list primes in increasing order. The number 1 has no prime factors at all.