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.

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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
Factors of

Factors Table

NumberFactors
4051, 3, 5, 9, 15, 27, 45, 81, 135, 405
4061, 2, 7, 14, 29, 58, 203, 406
4071, 11, 37, 407
4081, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408
4091, 409
4101, 2, 5, 10, 41, 82, 205, 410
4111, 3, 137, 411
4121, 2, 4, 103, 206, 412
4131, 7, 59, 413
4141, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
4151, 5, 83, 415
4161, 2, 4, 8, 13, 16, 26, 32, 52, 104, 208, 416
4171, 3, 139, 417
4181, 2, 11, 19, 22, 38, 209, 418
4191, 419
4201, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
4211, 421
4221, 2, 211, 422
4231, 3, 9, 47, 141, 423
4241, 2, 4, 8, 53, 106, 212, 424
4251, 5, 17, 25, 85, 425
4261, 2, 3, 6, 71, 142, 213, 426
4271, 7, 61, 427
4281, 2, 4, 107, 214, 428
4291, 3, 11, 13, 33, 39, 143, 429
4301, 2, 5, 10, 43, 86, 215, 430
4311, 431
4321, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 108, 144, 216, 432
4331, 433
4341, 2, 7, 14, 31, 62, 217, 434

FAQ

What are the Factors of 420?

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

How many factors does 420 have?

Number 420 has 24 factors

How many Factor Pairs does 420 have?

Number 420 has 12 factor pairs

See Also