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Factors of 624

Factors of 624 are integers that can be divided evenly into 624. There are overall 20 factors of 624 among which 624 is the biggest factor and its prime factors are 2, 3, 13. The sum of all factors of 624 is 1736.

  • All Factors of 624: 1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 39, 48, 52, 78, 104, 156, 208, 312 and 624
  • Prime Factors of 624: 2, 3, 13
  • Prime Factorization of 624: 24 × 31 × 131
  • Sum of Factors of 624: 1736
1. What Are the Factors of 624?
2. Factors of 624 by Prime Factorization
3. Factors of 624 in Pairs
4. FAQs on Factors of 624
Factors of 624

What are Factors of 624?

Factors of 624 are pairs of those numbers whose products result in 624. These factors are either prime numbers or composite numbers.

How to Find the Factors of 624?

To find the factors of 624, we will have to find the list of numbers that would divide 624 without leaving any remainder.

  • 624/6 = 104; therefore, 6 is a factor of 624 and 104 is also a factor of 624.
  • 624/48 = 13; therefore, 48 is a factor of 624 and 13 is also a factor of 624.
Similarly we can find other factors. Hence, the factors of 624 are 1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 39, 48, 52, 78, 104, 156, 208, 312, 624.

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Factors of 624 by Prime Factorization

The number 624 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 624. The first step is to divide the number 624 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.
  • 624 ÷ 2 = 312
  • 312 ÷ 2 = 156
  • 156 ÷ 2 = 78
  • 78 ÷ 2 = 39

Further dividing 39 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 39 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 624 can be written as 24 × 31 × 131 where 2, 3, 13 are prime.

 

Factors of 624 in Pairs

Pair factors of 624 are the pairs of numbers that when multiplied give the product 624. The factors of 624 in pairs are:

  • 1 × 624 = (1, 624)
  • 2 × 312 = (2, 312)
  • 3 × 208 = (3, 208)
  • 4 × 156 = (4, 156)
  • 6 × 104 = (6, 104)
  • 8 × 78 = (8, 78)
  • 12 × 52 = (12, 52)
  • 13 × 48 = (13, 48)
  • 16 × 39 = (16, 39)
  • 24 × 26 = (24, 26)

Negative pair factors of 624 are:

  • -1 × -624 = (-1, -624)
  • -2 × -312 = (-2, -312)
  • -3 × -208 = (-3, -208)
  • -4 × -156 = (-4, -156)
  • -6 × -104 = (-6, -104)
  • -8 × -78 = (-8, -78)
  • -12 × -52 = (-12, -52)
  • -13 × -48 = (-13, -48)
  • -16 × -39 = (-16, -39)
  • -24 × -26 = (-24, -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 624 Solved Examples

  1. Example 1: How many factors are there for 624?

    Solution:

    The factors of 624 are too many, therefore if we can find the prime factorization of 624, 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 624 = 24 × 31 × 131
    Therefore, the total number of factors are (4 + 1) × (1 + 1) × (1 + 1) = 5 × 2 × 2 = 20

  2. Example 2: Find the Least Common Multiple and Greatest Common Divisor (GCD) of 624 and 303.

    Solution:

    The factors of 624 are 1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 39, 48, 52, 78, 104, 156, 208, 312, 624 and factors of 303 are 1, 3, 101, 303.

    Therefore, the Least Common Multiple of 624 and 303 is 63024 and Greatest Common Divisor (GCD) of 624 and 303 is 3.

  3. Example 3: Find if 1, 4, 8, 13, 16, 24, 90 and 104 are factors of 624.

    Solution:

    When we divide 624 by 90 it leaves a remainder. Therefore, the number 90 is not a factor of 624. All numbers except 90 are factors of 624.

  4. Example 4: Find the product of all the prime factors of 624.

    Solution:

    Since, the prime factors of 624 are 2, 3, 13. Therefore, the product of prime factors = 2 × 3 × 13 = 78.

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FAQs on Factors of 624

What are the Factors of 624?

The factors of 624 are 1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 39, 48, 52, 78, 104, 156, 208, 312, 624 and its negative factors are -1, -2, -3, -4, -6, -8, -12, -13, -16, -24, -26, -39, -48, -52, -78, -104, -156, -208, -312, -624.

What is the Sum of all Factors of 624?

Sum of all factors of 624 = (24 + 1 - 1)/(2 - 1) × (31 + 1 - 1)/(3 - 1) × (131 + 1 - 1)/(13 - 1) = 1736

What are the Prime Factors of 624?

The prime factors of 624 are 2, 3, 13.

What is the Greatest Common Factor of 624 and 52?

The factors of 624 and 52 are 1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 39, 48, 52, 78, 104, 156, 208, 312, 624 and 1, 2, 4, 13, 26, 52 respectively.

Common factors of 624 and 52 are [1, 2, 4, 13, 26, 52].

Hence, the Greatest Common Factor (GCF) of 624 and 52 is 52.

How Many Factors of 420 are also common to the Factors of 624?

Since, the factors of 624 are 1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 39, 48, 52, 78, 104, 156, 208, 312, 624 and 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, 420.
Hence, [1, 2, 3, 4, 6, 12] are the common factors of 624 and 420.

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