Primes and divisors
A prime number can only be divided by 1 and itself. Find a number's prime factors and use them to find common denominators and simplify fractions.
The explanation is shown. Quick: prime yes/no, factors and GCD/LCM. Advanced: the neighbouring numbers, the nearest primes and the prime factors side by side.
Your numbers
Answer
Is 360 a prime number?
No
Prime factors
2^3 · 3^2 · 5
Number of divisors
24
Divisors: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360
How to work it out
- 1360 : 2 = 180
- 2180 : 2 = 90
- 390 : 2 = 45
- 445 : 3 = 15
- 515 : 3 = 5
- 65 : 5 = 1
The formula
2, 3, 5, 7, 11, 13, 17, 19, 23, 29 …
A prime number can only be divided by 1 and itself. 1 is not a prime.
360 = 2³ · 3² · 5
Every whole number above 1 can be written as a product of primes in exactly one way.
GCD(a, b) · LCM(a, b) = a · b
The GCD is found with Euclid's algorithm: divide, and continue with the remainder until the remainder is 0.
In depth: more numbers and “what if”
Previous prime: 359. Next prime: 367. Sum of the divisors: 1,170.
The neighbouring numbers
| Numbers | Prime? | Prime factors |
|---|---|---|
| 357 | No | 3 · 7 · 17 |
| 358 | No | 2 · 179 |
| 359 | Yes | 359 |
| 360 | No | 2^3 · 3^2 · 5 |
| 361 | No | 19^2 |
| 362 | No | 2 · 181 |
| 363 | No | 3 · 11^2 |
More: Numbers and percentages
- PercentPercentage of, how many per cent, percentage change, discount and VAT.
- FractionsAdd, subtract, multiply and divide fractions — and simplify the answer.
- Powers and rootsPowers, square roots, nth roots and numbers as powers of 10.
- Rounding and estimatingRound to decimals, tens or significant figures — and make an estimate.
- Order of operationsEnter a calculation and see it worked out step by step in the right order.
- Number systems and Roman numeralsBinary, hexadecimal and Roman numerals — converted both ways with working.