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Factors of 378

378 has 16 factors: 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189 and 378. Its prime factorization is 2 × 3³ × 7.

Factor pairs of 378

Factor×FactorProduct
1×378378
2×189378
3×126378
6×63378
7×54378
9×42378
14×27378
18×21378

Negative pairs work too: (−1) × (−378), (−2) × (−189), … = 378.

Number of factors
16
Factor pairs
8
Sum of factors
960
Prime or composite
Composite
Even or odd
Even
Perfect square
No
Prime factorization 2 × 3³ × 7

How to find the factors of 378

Test every whole number from 1 up to the square root of 378 (√378 ≈ 19.442). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

  • 378 ÷ 1 = 378 — so 1 and 378 are factors
  • 378 ÷ 2 = 189 — so 2 and 189 are factors
  • 378 ÷ 3 = 126 — so 3 and 126 are factors
  • 378 ÷ 4 = 94.5 — not a whole number
  • 378 ÷ 5 = 75.6 — not a whole number
  • 378 ÷ 6 = 63 — so 6 and 63 are factors
  • 378 ÷ 7 = 54 — so 7 and 54 are factors
  • 378 ÷ 8 = 47.25 — not a whole number
  • 378 ÷ 9 = 42 — so 9 and 42 are factors
  • 378 ÷ 10 = 37.8 — not a whole number
  • 378 ÷ 11 = 34.364 — not a whole number
  • 378 ÷ 12 = 31.5 — not a whole number
  • 378 ÷ 13 = 29.077 — not a whole number
  • 378 ÷ 14 = 27 — so 14 and 27 are factors
  • 378 ÷ 15 = 25.2 — not a whole number
  • 378 ÷ 16 = 23.625 — not a whole number
  • 378 ÷ 17 = 22.235 — not a whole number
  • 378 ÷ 18 = 21 — so 18 and 21 are factors
  • 378 ÷ 19 = 19.895 — not a whole number

Collecting both numbers from every successful division gives the complete list: 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189 and 378.

Prime factorization of 378

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

378 ÷ 2 = 189
189 ÷ 3 = 63
63 ÷ 3 = 21
21 ÷ 3 = 7
7 ÷ 7 = 1

The primes you divided by give 378 = 2 × 3³ × 7. From the exponents you can also count the factors without listing them: (1 + 1) × (3 + 1) × (1 + 1) = 16.

Properties of 378

  • 378 is a composite number.
  • The sum of all its factors is 960; the sum of its proper factors (excluding 378) is 582, which makes it a abundant number (its proper factors add up to more than itself).
  • 378 is not a perfect square, so its factors pair up evenly.
  • Multiples of 378 include 756, 1,134, 1,512, 1,890 and so on.

Factors vs. multiples

Factors of 378 are the numbers that divide into it; multiples of 378 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 378?

The factors of 378 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189 and 378. Each of these divides 378 with no remainder.

How many factors does 378 have?

378 has 16 positive factors, which form 8 factor pairs. Counting negative factors as well doubles that to 32.

What is the prime factorization of 378?

378 = 2 × 3³ × 7. Its distinct prime factors are 2, 3 and 7.

Is 378 a prime number?

No. 378 is composite because it has 16 factors, more than the two a prime number has.