Prime Factorization
Break any whole number into its prime factor building blocks.
A prime number is a whole number greater than 1 that has exactly two factors: 1 and itself. Primes are the "atoms" of arithmetic — every integer greater than 1 can be written as a unique product of primes (fundamental theorem of arithmetic).
- 1Check if the number is greater than 1
- 2Try dividing by every integer from 2 up to √n
- 3If none divide evenly, the number is prime
- 4If any divide evenly, it is composite (not prime)
17=PrimeNot divisible by 2, 3
51=Composite51 = 3 × 17
97=PrimeNot divisible by 2,3,5,7
| Range | Prime numbers |
|---|---|
| 1–20 | 2, 3, 5, 7, 11, 13, 17, 19 |
| 21–50 | 23, 29, 31, 37, 41, 43, 47 |
| 51–80 | 53, 59, 61, 67, 71, 73, 79 |
| 81–100 | 83, 89, 97 |
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Fun Fact
The largest known prime (as of 2024) has over 41 million digits. It was discovered using distributed computing. There are infinitely many primes — proved by Euclid around 300 BC.
References
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