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Factors of 372

Factors of 372 are integers that can be divided evenly into 372. There are overall 12 factors of 372 among which 372 is the biggest factor and 2, 3, 31 are its prime factors. The Prime Factorization of 372 is 22 × 31 × 311.

  • All Factors of 372: 1, 2, 3, 4, 6, 12, 31, 62, 93, 124, 186 and 372
  • Prime Factors of 372: 2, 3, 31
  • Prime Factorization of 372: 22 × 31 × 311
  • Sum of Factors of 372: 896
1. What Are the Factors of 372?
2. Factors of 372 by Prime Factorization
3. Factors of 372 in Pairs
4. FAQs on Factors of 372
Factors of 372

What are Factors of 372?

Factors of 372 are pairs of those numbers whose products result in 372. These factors are either prime numbers or composite numbers.

How to Find the Factors of 372?

To find the factors of 372, we will have to find the list of numbers that would divide 372 without leaving any remainder.

  • 372/372 = 1; therefore, 372 is a factor of 372.
  • 372/62 = 6; therefore, 62 is a factor of 372.
Similarly we can find other factors. Hence, the factors of 372 are 1, 2, 3, 4, 6, 12, 31, 62, 93, 124, 186, 372.

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Factors of 372 by Prime Factorization

The number 372 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 372. The first step is to divide the number 372 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.
  • 372 ÷ 2 = 186
  • 186 ÷ 2 = 93

Further dividing 93 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 93 by the next smallest prime factor. We stop ultimately if the next prime factor doesn't exist or when we can't divide any further.

So, the prime factorization of 372 can be written as 22 × 31 × 311 where 2, 3, 31 are prime.

 

Factors of 372 in Pairs

Pair factors of 372 are the pairs of numbers that when multiplied give the product 372. The factors of 372 in pairs are:

  • 1 × 372 = (1, 372)
  • 2 × 186 = (2, 186)
  • 3 × 124 = (3, 124)
  • 4 × 93 = (4, 93)
  • 6 × 62 = (6, 62)
  • 12 × 31 = (12, 31)

Negative pair factors of 372 are:

  • -1 × -372 = (-1, -372)
  • -2 × -186 = (-2, -186)
  • -3 × -124 = (-3, -124)
  • -4 × -93 = (-4, -93)
  • -6 × -62 = (-6, -62)
  • -12 × -31 = (-12, -31)

NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.

Factors of 372 Solved Examples

  1. Example 1: How many factors are there for 372?

    Solution:

    The factors of 372 are too many, therefore if we can find the prime factorization of 372, then the total number of factors can be calculated using the formula shown below.
    If the prime factorization of the number is ax × by × cz where a, b, c are prime, then the total number of factors can be given by (x + 1)(y + 1)(z + 1).

    Prime Factorization of 372 = 22 × 31 × 311
    Therefore, the total number of factors are (2 + 1) × (1 + 1) × (1 + 1) = 3 × 2 × 2 = 12

  2. Example 2: Find the Least Common Multiple (LCM) and Greatest Common Factor (GCF) of 372 and 167.

    Solution:

    The factors of 372 are 1, 2, 3, 4, 6, 12, 31, 62, 93, 124, 186, 372 and factors of 167 are 1, 167.

    Therefore, the Least Common Multiple (LCM) of 372 and 167 is 62124 and Greatest Common Factor (GCF) of 372 and 167 is 1.

  3. Example 3: Find if 2, 3, 6, 12, 93, 186 and 372 are factors of 372.

    Solution:

    When we divide 372 by 2, 3, 6, 12, 93, 186, 372 it doesn't leave any remainder. Therefore, 2, 3, 6, 12, 93, 186, 372 are factors of 372.

  4. Example 4: Find the product of all the prime factors of 372.

    Solution:

    Since, the prime factors of 372 are 2, 3, 31. Therefore, the product of prime factors = 2 × 3 × 31 = 186.

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FAQs on Factors of 372

What are the Factors of 372?

The factors of 372 are 1, 2, 3, 4, 6, 12, 31, 62, 93, 124, 186, 372 and its negative factors are -1, -2, -3, -4, -6, -12, -31, -62, -93, -124, -186, -372.

What is the Sum of Factors of 372?

Sum of all factors of 372 = (22 + 1 - 1)/(2 - 1) × (31 + 1 - 1)/(3 - 1) × (311 + 1 - 1)/(31 - 1) = 896

What are Pair Factors of 372?

The pair factors of 372 are (1, 372), (2, 186), (3, 124), (4, 93), (6, 62), (12, 31).

What is the Greatest Common Factor of 372 and 46?

The factors of 372 and 46 are 1, 2, 3, 4, 6, 12, 31, 62, 93, 124, 186, 372 and 1, 2, 23, 46 respectively.

Common factors of 372 and 46 are [1, 2].

Hence, the Greatest Common Factor (GCF) of 372 and 46 is 2.

What are the Common Factors of 372 and 47?

Since, the factors of 372 are 1, 2, 3, 4, 6, 12, 31, 62, 93, 124, 186, 372 and factors of 47 are 1, 47. Hence, 372 and 47 have only one common factor which is 1. Therefore, 372 and 47 are co-prime.

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