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    Prime Factorization

    Prime Factorization Calculator

    "Prime Factorization" Calculator

    Prime Factors of

    How to Find the Prime Factorization of a Number

    How to factor 24 into primes

    242
    122
    62
    33
    1

    24 = 23 × 3

    Left: what is left; right: the smallest prime that divides it; 1 at the bottom.

    Second way — factor tree
    242122623
    Rule: divide by the smallest prime that divides the number evenly (2, 3, 5, 7, …) until 1 is left; the divisors to the right of the line are the answer.
    Most asked
    NumberPrime factorization
    100,00025 × 55
    2,24823 × 281
    999,1233, 333041
    2,0022, 7, 11, 13
    8,00026 × 53
    90,72025 × 34 × 5 × 7

    See Also

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    FAQ

    What is prime factorization?

    It is writing a number as a product of prime numbers only. For 24 the factorization is 2 × 2 × 2 × 3, which is usually written as 2³ × 3.

    Can a number have two different prime factorizations?

    No. The fundamental theorem of arithmetic says that every integer greater than 1 breaks down into primes in exactly one way, apart from the order of the factors.

    How do you factor a number by hand?

    Divide by the smallest prime that fits, again and again: 1,260 ÷ 2 = 630, ÷ 2 = 315, ÷ 3 = 105, ÷ 3 = 35, ÷ 5 = 7, and 7 is already prime, so 1,260 = 2² × 3² × 5 × 7. You can stop testing divisors once the square of the divisor exceeds what is left.