Break any whole number up to 9,007,199,254,740,991 into prime factors. See the exponent form, a division ladder, every divisor and the divisor count.
The prime factorization of a whole number is the unique way to write it as a product of prime numbers: 360 = 2 × 2 × 2 × 3 × 3 × 5, or 2^3 × 3^2 × 5 in exponent form. The fundamental theorem of arithmetic says every whole number from 2 up has exactly one such product, apart from the order of the factors. A prime has only itself as a factorization, so 97 shows as prime. Type a number and the page gives the product, the exponent form, whether it is prime or composite, and the steps.
It divides out 2 and 3, then tries every candidate of the form 6k - 1 and 6k + 1 up to 65,536, because every prime above 3 has that form. What remains is tested with the Miller-Rabin test using the first 13 primes (2 through 41) as bases, which is proven exact for every number below 3.3 × 10^24, so it is always right for the 2^53 range. A composite remainder is split with Pollard's rho method, which finds a factor in about the fourth root of the number's size in steps. The page needs a browser with BigInt support (all current ones have it) and shows a short notice if yours does not.
The table divides by the smallest prime at each step until 1 is left, the same as a factor tree read in a straight line: 360 ÷ 2 = 180, 180 ÷ 2 = 90, and so on. From the exponents the page also builds every divisor. If n = p^a × q^b, the number of divisors is (a + 1)(b + 1), so 360 has (3 + 1)(2 + 1)(1 + 1) = 24 divisors, and the sum of divisors is the product of (p^(e+1) - 1)/(p - 1) for each prime, which gives 1,170. Factor pairs list each divisor with its partner, such as 18 × 20.
Fill in the optional second number to get the greatest common divisor (GCD, also called HCF) and the least common multiple (LCM) of the two, worked with the identity gcd × lcm = a × b. The LCM is exact even when it passes 2^53. The input limit is 9,007,199,254,740,991, which is 2^53 - 1, the largest safe integer this Number-based calculator accepts. Nothing you type is stored or sent anywhere. To test one number for primality at larger sizes use the prime number checker, and for several numbers at once use the GCD and LCM calculator.
360 = 2^3 × 3^2 × 5, which is 2 × 2 × 2 × 3 × 3 × 5. It has (3 + 1)(2 + 1)(1 + 1) = 24 divisors, and they add up to 1,170.
Divide by the smallest prime that goes in exactly, write it down, and repeat on the quotient until you reach 1. For 84: 84 ÷ 2 = 42, 42 ÷ 2 = 21, 21 ÷ 3 = 7, 7 is prime, so 84 = 2^2 × 3 × 7.
A number is prime when its factorization is just itself, so it has exactly 2 divisors. If a number has no divisor up to its square root it is prime: 97 has none up to 9, so it is prime. This page says so and shows a divisor count of 2.
Add 1 to each exponent in the prime factorization and multiply. 2^4 × 3 = 48 has (4 + 1)(1 + 1) = 10 divisors: 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48.
9,007,199,254,740,991, which is 2^53 - 1. It factors as 6,361 × 69,431 × 20,394,401. Above that, JavaScript numbers are no longer guaranteed exact for every whole number, so the page asks for a smaller one.
Type a second number. For 360 and 84 the GCD is 12 and the LCM is 2,520, since 360 × 84 = 30,240 = 12 × 2,520.