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Factors of 364

Factors of 364 are the list of integers that we can split evenly into 364. There are overall 12 factors of 364 among which 364 is the biggest factor and 2, 7, 13 are its prime factors. The sum of all factors of 364 is 784.

  • All Factors of 364: 1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182 and 364
  • Prime Factors of 364: 2, 7, 13
  • Prime Factorization of 364: 22 × 71 × 131
  • Sum of Factors of 364: 784
1. What Are the Factors of 364?
2. Factors of 364 by Prime Factorization
3. Factors of 364 in Pairs
4. FAQs on Factors of 364
Factors of 364

What are Factors of 364?

Factors of 364 are pairs of those numbers whose products result in 364. These factors are either prime numbers or composite numbers.

How to Find the Factors of 364?

To find the factors of 364, we will have to find the list of numbers that would divide 364 without leaving any remainder.

  • 364/4 = 91; therefore, 4 is a factor of 364 and 91 is also a factor of 364.
  • 364/182 = 2; therefore, 182 is a factor of 364 and 2 is also a factor of 364.
Similarly we can find other factors. Hence, the factors of 364 are 1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182, 364.

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Factors of 364 by Prime Factorization

The number 364 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 364. The first step is to divide the number 364 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.
  • 364 ÷ 2 = 182
  • 182 ÷ 2 = 91

Further dividing 91 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 91 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 364 can be written as 22 × 71 × 131 where 2, 7, 13 are prime.

 

Factors of 364 in Pairs

Pair factors of 364 are the pairs of numbers that when multiplied give the product 364. The factors of 364 in pairs are:

  • 1 × 364 = (1, 364)
  • 2 × 182 = (2, 182)
  • 4 × 91 = (4, 91)
  • 7 × 52 = (7, 52)
  • 13 × 28 = (13, 28)
  • 14 × 26 = (14, 26)

Negative pair factors of 364 are:

  • -1 × -364 = (-1, -364)
  • -2 × -182 = (-2, -182)
  • -4 × -91 = (-4, -91)
  • -7 × -52 = (-7, -52)
  • -13 × -28 = (-13, -28)
  • -14 × -26 = (-14, -26)

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

Factors of 364 Solved Examples

  1. Example 1: How many factors are there for 364?

    Solution:

    The factors of 364 are too many, therefore if we can find the prime factorization of 364, 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 364 = 22 × 71 × 131
    Therefore, the total number of factors are (2 + 1) × (1 + 1) × (1 + 1) = 3 × 2 × 2 = 12

  2. Example 2: Find the Lowest Common Multiple (LCM) and Greatest Common Divisor (GCD) of 364 and 347.

    Solution:

    The factors of 364 are 1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182, 364 and factors of 347 are 1, 347.

    Therefore, the Lowest Common Multiple (LCM) of 364 and 347 is 126308 and Greatest Common Divisor (GCD) of 364 and 347 is 1.

  3. Example 3: Find if 1, 7, 13, 14, 52, 230 and 364 are factors of 364.

    Solution:

    When we divide 364 by 230 it leaves a remainder. Therefore, the number 230 is not a factor of 364. All numbers except 230 are factors of 364.

  4. Example 4: Find the product of all the prime factors of 364.

    Solution:

    Since, the prime factors of 364 are 2, 7, 13. Therefore, the product of prime factors = 2 × 7 × 13 = 182.

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FAQs on Factors of 364

What are the Factors of 364?

The factors of 364 are 1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182, 364 and its negative factors are -1, -2, -4, -7, -13, -14, -26, -28, -52, -91, -182, -364.

What is the Sum of Factors of 364?

Sum of all factors of 364 = (22 + 1 - 1)/(2 - 1) × (71 + 1 - 1)/(7 - 1) × (131 + 1 - 1)/(13 - 1) = 784

What Numbers are the Prime Factors of 364?

The prime factors of 364 are 2, 7, 13.

What is the Greatest Common Factor of 364 and 36?

The factors of 364 and 36 are 1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182, 364 and 1, 2, 3, 4, 6, 9, 12, 18, 36 respectively.

Common factors of 364 and 36 are [1, 2, 4].

Hence, the Greatest Common Factor of 364 and 36 is 4.

How Many Factors of 364 are also common to the Factors of 323?

Since, the factors of 364 are 1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182, 364 and factors of 323 are 1, 17, 19, 323. Hence, 364 and 323 have only one common factor which is 1. Therefore, 364 and 323 are co-prime.

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