Factors of 420
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What are the Factors of 420?
Answer
Factors of 420:
1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
(number 420 has 24 factors)
Factor Pairs of 420
A Factor Pair of number 420 is a combination of two factors which can be multiplied together to equal 420.
List of all possible Factor Pairs of 420:
- 1 × 420 = 420
- 2 × 210 = 420
- 3 × 140 = 420
- 4 × 105 = 420
- 5 × 84 = 420
- 6 × 70 = 420
- 7 × 60 = 420
- 10 × 42 = 420
- 12 × 35 = 420
- 14 × 30 = 420
- 15 × 28 = 420
- 20 × 21 = 420
How to find the Factors of 420
Divide 420 by every whole number from 1 up to 20. Each division without a remainder gives a factor and its pair. There is no point going further: 21 × 21 = 441 is already greater than 420, so any larger divisor would pair with a smaller one you have already checked.
- 420 ÷ 1 = 420 — factors 1 and 420
- 420 ÷ 2 = 210 — factors 2 and 210
- 420 ÷ 3 = 140 — factors 3 and 140
- 420 ÷ 4 = 105 — factors 4 and 105
- 420 ÷ 5 = 84 — factors 5 and 84
- 420 ÷ 6 = 70 — factors 6 and 70
- 420 ÷ 7 = 60 — factors 7 and 60
- 420 ÷ 8 — remainder 4, not a factor
- 420 ÷ 9 — remainder 6, not a factor
- 420 ÷ 10 = 42 — factors 10 and 42
- 420 ÷ 11 — remainder 2, not a factor
- 420 ÷ 12 = 35 — factors 12 and 35
- 420 ÷ 13 — remainder 4, not a factor
- 420 ÷ 14 = 30 — factors 14 and 30
- 420 ÷ 15 = 28 — factors 15 and 28
- 420 ÷ 16 — remainder 4, not a factor
- 420 ÷ 17 — remainder 12, not a factor
- 420 ÷ 18 — remainder 6, not a factor
- 420 ÷ 19 — remainder 2, not a factor
- 420 ÷ 20 = 21 — factors 20 and 21
Why 420 has exactly 24 factors
The count follows from the prime factorization: add 1 to each exponent and multiply. Counting the divisors this way needs no trial division at all, however large the number is.
420 = 22 × 3 × 5 × 7
(2 + 1) × (1 + 1) × (1 + 1) × (1 + 1) = 24
Step-by-step factorization: Prime factors of 420.
Found an error in the calculation or the information?
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See Also
- Prime Number Checker - Find out whether a given number is Prime or not
- Prime Factorization - Prime Factorization Calculator
- Prime Numbers List - List of all Prime Numbers - how many Prime numbers are between
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Factors Table
| Number | Factors |
|---|---|
| 405 | 1, 3, 5, 9, 15, 27, 45, 81, 135, 405 |
| 406 | 1, 2, 7, 14, 29, 58, 203, 406 |
| 407 | 1, 11, 37, 407 |
| 408 | 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408 |
| 409 | 1, 409 |
| 410 | 1, 2, 5, 10, 41, 82, 205, 410 |
| 411 | 1, 3, 137, 411 |
| 412 | 1, 2, 4, 103, 206, 412 |
| 413 | 1, 7, 59, 413 |
| 414 | 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414 |
| 415 | 1, 5, 83, 415 |
| 416 | 1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 208, 416 |
| 417 | 1, 3, 139, 417 |
| 418 | 1, 2, 11, 19, 22, 38, 209, 418 |
| 419 | 1, 419 |
| 420 | 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420 |
| 421 | 1, 421 |
| 422 | 1, 2, 211, 422 |
| 423 | 1, 3, 9, 47, 141, 423 |
| 424 | 1, 2, 4, 8, 53, 106, 212, 424 |
| 425 | 1, 5, 17, 25, 85, 425 |
| 426 | 1, 2, 3, 6, 71, 142, 213, 426 |
| 427 | 1, 7, 61, 427 |
| 428 | 1, 2, 4, 107, 214, 428 |
| 429 | 1, 3, 11, 13, 33, 39, 143, 429 |
| 430 | 1, 2, 5, 10, 43, 86, 215, 430 |
| 431 | 1, 431 |
| 432 | 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 108, 144, 216, 432 |
| 433 | 1, 433 |
| 434 | 1, 2, 7, 14, 31, 62, 217, 434 |
About "Factors of a Number" Calculator
This calculator will help you find all factors of a given number. For example, it can help you find out what are the Factors of 420? (The answer is: 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420). Pick the number (e.g. '420'). After that hit the 'Find' button.
The Factors of a number are numbers that divides initial number evenly, with no remainder
"Factors of a Number" Calculator