Free Maths Calculator

Prime Factor Calculator

Break any number into its prime factors with a division ladder: divide by the smallest prime again and again until you reach 1, then collect the answer in index form with powers. Product of prime factors questions appear on almost every GCSE non calculator paper, so the layout here matches exam working.

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    Worked Example

    Write 60 as a product of its prime factors in index form.

    1. Divide by the smallest prime that fits:60 ÷ 2 = 30, then 30 ÷ 2 = 15
    2. 2 no longer fits, so move up:15 ÷ 3 = 5, and 5 is prime, so stop
    3. Read the ladder:60 = 2 × 2 × 3 × 5, which is 2² × 3 × 5 in index form

    Answer: 60 = 2² × 3 × 5

    Try These Yourself

    Write 36 as a product of prime factors in index form.Show answerHide answer

    Answer: 2² × 3²

    36 = 2 × 2 × 3 × 3.

    Write 100 as a product of prime factors in index form.Show answerHide answer

    Answer: 2² × 5²

    100 = 2 × 2 × 5 × 5.

    Is 91 prime?Show answerHide answer

    Answer: No, 91 = 7 × 13

    Try the primes in order: 2, 3 and 5 fail, but 7 fits.