qcalculate

Prime Factorization Calculator

Break a whole number into its prime factors and watch the factor tree grow, one division at a time, ending with the answer in exponent form.

Prime factorization

360 = 2³ × 3² × 5

360 = 2³ × 3² × 5.

Show me how

All steps as text

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    How to find prime factors

    1. Divide by the smallest prime that goes in exactly: 2 if the number is even, 3 if its digits add up to a multiple of 3, 5 if it ends in 0 or 5, then 7, 11, 13 and so on.
    2. Keep dividing what is left the same way.
    3. Stop when what is left is a prime. The primes you divided by, and that last one, are the prime factors.

    For 360: 360 ÷ 2 = 180, 180 ÷ 2 = 90, 90 ÷ 2 = 45, 45 ÷ 3 = 15, 15 ÷ 3 = 5, and 5 is prime. So 360 = 2 × 2 × 2 × 3 × 3 × 5 = 2³ × 3² × 5.

    Questions

    Is 1 a prime number?

    No. A prime has exactly two factors, 1 and itself; 1 has only one. That is why 1 never appears in a prime factorization.

    Does it matter which prime I start with?

    No. Every whole number above 1 has exactly one set of prime factors, so any order gives the same answer. Starting with the smallest keeps the tree tidy.

    What are prime factors used for?

    Finding the GCF and LCM, simplifying fractions and square roots, and checking whether a number is a perfect square (every power is even) or cube.