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Factors of 504

Factors of 504 are the list of integers that can be evenly divided into 504. There are 24 factors of 504 of which 504 itself is the biggest factor and its prime factors are 2, 3, 7 The Prime Factorization of 504 is 23 × 32 × 71.

  • All Factors of 504: 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 168, 252 and 504
  • Prime Factors of 504: 2, 3, 7
  • Prime Factorization of 504: 23 × 32 × 71
  • Sum of Factors of 504: 1560
1. What Are the Factors of 504?
2. Factors of 504 by Prime Factorization
3. Factors of 504 in Pairs
4. FAQs on Factors of 504
Factors of 504

What are Factors of 504?

Factors of 504 are pairs of those numbers whose products result in 504. These factors are either prime numbers or composite numbers.

How to Find the Factors of 504?

To find the factors of 504, we will have to find the list of numbers that would divide 504 without leaving any remainder.

  • 504/12 = 42; therefore, 12 is a factor of 504 and 42 is also a factor of 504.
  • 504/126 = 4; therefore, 126 is a factor of 504 and 4 is also a factor of 504.
Similarly we can find other factors. Hence, the factors of 504 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 168, 252, 504.

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Factors of 504 by Prime Factorization

The number 504 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 504. The first step is to divide the number 504 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.
  • 504 ÷ 2 = 252
  • 252 ÷ 2 = 126
  • 126 ÷ 2 = 63

Further dividing 63 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 63 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 504 can be written as 23 × 32 × 71 where 2, 3, 7 are prime.

 

Factors of 504 in Pairs

Pair factors of 504 are the pairs of numbers that when multiplied give the product 504. The factors of 504 in pairs are:

  • 1 × 504 = (1, 504)
  • 2 × 252 = (2, 252)
  • 3 × 168 = (3, 168)
  • 4 × 126 = (4, 126)
  • 6 × 84 = (6, 84)
  • 7 × 72 = (7, 72)
  • 8 × 63 = (8, 63)
  • 9 × 56 = (9, 56)
  • 12 × 42 = (12, 42)
  • 14 × 36 = (14, 36)
  • 18 × 28 = (18, 28)
  • 21 × 24 = (21, 24)

Negative pair factors of 504 are:

  • -1 × -504 = (-1, -504)
  • -2 × -252 = (-2, -252)
  • -3 × -168 = (-3, -168)
  • -4 × -126 = (-4, -126)
  • -6 × -84 = (-6, -84)
  • -7 × -72 = (-7, -72)
  • -8 × -63 = (-8, -63)
  • -9 × -56 = (-9, -56)
  • -12 × -42 = (-12, -42)
  • -14 × -36 = (-14, -36)
  • -18 × -28 = (-18, -28)
  • -21 × -24 = (-21, -24)

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

Factors of 504 Solved Examples

  1. Example 1: How many factors are there for 504?

    Solution:

    The factors of 504 are too many, therefore if we can find the prime factorization of 504, 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 504 = 23 × 32 × 71
    Therefore, the total number of factors are (3 + 1) × (2 + 1) × (1 + 1) = 4 × 3 × 2 = 24

  2. Example 2: Find the Least Common Multiple (LCM) and Greatest Common Divisor (GCD) of 504 and 463.

    Solution:

    The factors of 504 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 168, 252, 504 and factors of 463 are 1, 463.

    Therefore, the Least Common Multiple (LCM) of 504 and 463 is 233352 and Greatest Common Divisor (GCD) of 504 and 463 is 1.

  3. Example 3: Find if 1, 2, 4, 7, 18, 36, 49 and 63 are factors of 504.

    Solution:

    When we divide 504 by 49 it leaves a remainder. Therefore, the number 49 is not a factor of 504. All numbers except 49 are factors of 504.

  4. Example 4: Find the product of all the prime factors of 504.

    Solution:

    Since, the prime factors of 504 are 2, 3, 7. Therefore, the product of prime factors = 2 × 3 × 7 = 42.

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FAQs on Factors of 504

What are the Factors of 504?

The factors of 504 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 168, 252, 504 and its negative factors are -1, -2, -3, -4, -6, -7, -8, -9, -12, -14, -18, -21, -24, -28, -36, -42, -56, -63, -72, -84, -126, -168, -252, -504.

What is the Sum of all Factors of 504?

Sum of all factors of 504 = (23 + 1 - 1)/(2 - 1) × (32 + 1 - 1)/(3 - 1) × (71 + 1 - 1)/(7 - 1) = 1560

What Numbers are the Prime Factors of 504?

The prime factors of 504 are 2, 3, 7.

What is the Greatest Common Factor of 504 and 26?

The factors of 504 and 26 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 168, 252, 504 and 1, 2, 13, 26 respectively.

Common factors of 504 and 26 are [1, 2].

Hence, the GCF of 504 and 26 is 2.

How Many Factors of 165 are also common to the Factors of 504?

Since, the factors of 504 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 168, 252, 504 and the factors of 165 are 1, 3, 5, 11, 15, 33, 55, 165.
Hence, [1, 3] are the common factors of 504 and 165.

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