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Number-Theory · Prime-Factorization

Prime factorization of 360

360

Step by step

  1. 360

    Factor 360 by dividing out the smallest prime that goes in, again and again.

  2. 360 = 2 \times 180

    2 is the smallest prime dividing 360.

  3. 180 = 2 \times 90

    2 is the smallest prime dividing 180.

  4. 90 = 2 \times 45

    2 is the smallest prime dividing 90.

  5. 45 = 3 \times 15

    3 is the smallest prime dividing 45.

  6. 15 = 3 \times 5

    3 is the smallest prime dividing 15. That leaves a prime, so we stop.

  7. 5 = 5 \times 1

    5 is the smallest prime dividing 5. That leaves a prime, so we stop.

  8. 360 = 2^{3} \times 3^{2} \times 5

    Collect equal primes as powers.

  9. d(360) = (3+1) \cdot (2+1) \cdot (1+1) = 24

    Bonus: the number of divisors is the product of (exponent + 1) over the prime powers.

Reveal the answer
360 = 2^{3} \times 3^{2} \times 5