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Prime factorisation
Every integer is a product of primes in exactly one way.
Divide out the smallest prime again and again until only 1 is left; the primes you removed, with their multiplicities, are the unique prime factorisation. The factor tree below is drawn from those divisions. From it you can read the number of divisors and the gcd or lcm with any other number.
ਕੰਮ ਉਦਾਹਰਨ: prime factorization of 360
ਕਦਮ ਦਰ ਕਦਮ
- 360
Factor 360 by dividing out the smallest prime that goes in, again and again.
- 360 = 2 \times 180
2 is the smallest prime dividing 360.
- 180 = 2 \times 90
2 is the smallest prime dividing 180.
- 90 = 2 \times 45
2 is the smallest prime dividing 90.
- 45 = 3 \times 15
3 is the smallest prime dividing 45.
- 15 = 3 \times 5
3 is the smallest prime dividing 15. That leaves a prime, so we stop.
- 5 = 5 \times 1
5 is the smallest prime dividing 5. That leaves a prime, so we stop.
- 360 = 2^{3} \times 3^{2} \times 5
Collect equal primes as powers.
- 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.
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Prime numbersGCD and LCMModular arithmeticDivisorsSequencesNumber bases