Math Calculator: Primes, GCF, LCM, Statistics, Logs

Key facts

Every whole number greater than 1 is a product of primes in exactly one way, apart from order: 360 = 2³ × 3² × 5.
The number of factors comes from the exponents: add 1 to each and multiply, so 360 has 4 × 3 × 2 = 24 factors.
A number is a perfect square exactly when every exponent in its prime factorization is even: 3,600 = 2⁴ × 3² × 5².

Whole number

Any whole number up to 20 digits.

Try

360 as a product of primes

2³ × 3² × 5

360 = 2³ × 3² × 5, so it has 24 factors and is composite.

222335

Factors: 24
Square root: ≈ 18.9737
Sum of factors: 1,170

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Worked example: 360Divide by primes, then read off the factors and the square root

Divide by the smallest prime that goes in exactly, and repeat with the quotient until it is 1.
360 ÷ 2 = 180
180 ÷ 2 = 90
90 ÷ 2 = 45
45 ÷ 3 = 15
15 ÷ 3 = 5
5 ÷ 5 = 1
Collect the primes you divided by; repeated ones become powers.
360 = 2 × 2 × 2 × 3 × 3 × 5 = 2³ × 3² × 5
Count the factors from the exponents: add 1 to each and multiply, (3 + 1) × (2 + 1) × (1 + 1) = 24. Each factor picks how many of each prime to use.
360 is not a perfect square (not every exponent is even), so √360 is irrational: about 18.973666.
The nearest primes: 359 below and 367 above.

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MethodChecked against 13 worked examplesUpdated Oct 2026

How this works

Method

Whole numbers up to 10²⁰ are exact big integers: primes are checked with a deterministic Miller–Rabin test, numbers are split into primes by trial division and then Pollard’s rho method, and the GCF comes from Euclid’s algorithm. The mean, median and variances are exact fractions of the numbers you type, and only the standard deviation, a square root, is rounded. Powers are exact up to 100,000 digits; roots and logarithms are exact when the answer is rational and otherwise shown as approximate.

How it’s tested

13 worked examples for this page are checked by automated tests before every release: given the inputs, the tool must show the expected answer.

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Changes

8 Oct 2026 First published, with ten calculators: GCF, LCM, factors, prime checker, prime factorization, mean, median and mode, standard deviation, variance, exponents and logarithms.

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Factors and primes · Averages and spread · Powers and logarithms

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Averages and spread

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Frequently Asked Questions

What does the number facts calculator show?

Type any whole number up to 20 digits and it shows the number as a product of primes, whether it is prime, how many factors it has and what they add up to, its square root (exact for a perfect square) and the nearest primes, with the division steps that find them.

Which calculators are in this family?

GCF and LCM, all factors of a number, a prime number checker and prime factorization; mean, median and mode, standard deviation and variance; and exponents and logarithms. Pick one from the Calculator menu at the top of the tool, or open the full list below.

How big can the numbers be?

The factor and prime tools take whole numbers up to 10²⁰ and work with exact big integers, using a Miller–Rabin test for primes and Pollard’s rho method to split large numbers. Exponents give exact answers up to 100,000 digits.

Are the statistics exact?

The mean, median and both variances are worked out as exact fractions from the numbers you type, so 0.1, 0.2 and 0.3 average exactly 0.2. Only the standard deviation, a square root, is rounded, and it is correct to every digit shown.