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Factors of 420

420 has 24 factors: 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210 and 420. Its prime factorization is 2² × 3 × 5 × 7.

Factor pairs of 420

Factor×FactorProduct
1×420420
2×210420
3×140420
4×105420
5×84420
6×70420
7×60420
10×42420
12×35420
14×30420
15×28420
20×21420

Negative pairs work too: (−1) × (−420), (−2) × (−210), … = 420.

Number of factors
24
Factor pairs
12
Sum of factors
1,344
Prime or composite
Composite
Even or odd
Even
Perfect square
No
Prime factorization 2² × 3 × 5 × 7

How to find the factors of 420

Test every whole number from 1 up to the square root of 420 (√420 ≈ 20.494). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

  • 420 ÷ 1 = 420 — so 1 and 420 are factors
  • 420 ÷ 2 = 210 — so 2 and 210 are factors
  • 420 ÷ 3 = 140 — so 3 and 140 are factors
  • 420 ÷ 4 = 105 — so 4 and 105 are factors
  • 420 ÷ 5 = 84 — so 5 and 84 are factors
  • 420 ÷ 6 = 70 — so 6 and 70 are factors
  • 420 ÷ 7 = 60 — so 7 and 60 are factors
  • 420 ÷ 8 = 52.5 — not a whole number
  • 420 ÷ 9 = 46.667 — not a whole number
  • 420 ÷ 10 = 42 — so 10 and 42 are factors
  • 420 ÷ 11 = 38.182 — not a whole number
  • 420 ÷ 12 = 35 — so 12 and 35 are factors
  • 420 ÷ 13 = 32.308 — not a whole number
  • 420 ÷ 14 = 30 — so 14 and 30 are factors
  • 420 ÷ 15 = 28 — so 15 and 28 are factors
  • 420 ÷ 16 = 26.25 — not a whole number
  • 420 ÷ 17 = 24.706 — not a whole number
  • 420 ÷ 18 = 23.333 — not a whole number
  • 420 ÷ 19 = 22.105 — not a whole number
  • 420 ÷ 20 = 21 — so 20 and 21 are factors

Collecting both numbers from every successful division gives the complete list: 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210 and 420.

Prime factorization of 420

Divide by the smallest prime that fits, and keep going until the quotient is 1:

420 ÷ 2 = 210
210 ÷ 2 = 105
105 ÷ 3 = 35
35 ÷ 5 = 7
7 ÷ 7 = 1

The primes you divided by give 420 = 2² × 3 × 5 × 7. From the exponents you can also count the factors without listing them: (2 + 1) × (1 + 1) × (1 + 1) × (1 + 1) = 24.

Properties of 420

  • 420 is a composite number.
  • The sum of all its factors is 1,344; the sum of its proper factors (excluding 420) is 924, which makes it a abundant number (its proper factors add up to more than itself).
  • 420 is not a perfect square, so its factors pair up evenly.
  • Multiples of 420 include 840, 1,260, 1,680, 2,100 and so on.

Factors vs. multiples

Factors of 420 are the numbers that divide into it; multiples of 420 are the numbers it divides into. Every number has a limited set of factors but infinitely many multiples. To work with any other number, use the factors calculator, or find shared factors with the GCF calculator.

Frequently asked questions

What are the factors of 420?

The factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210 and 420. Each of these divides 420 with no remainder.

How many factors does 420 have?

420 has 24 positive factors, which form 12 factor pairs. Counting negative factors as well doubles that to 48.

What is the prime factorization of 420?

420 = 2² × 3 × 5 × 7. Its distinct prime factors are 2, 3, 5 and 7.

Is 420 a prime number?

No. 420 is composite because it has 24 factors, more than the two a prime number has.