Factors of 504 in pair are (1, 504) , (2, 252) , (3, 168) , (4, 126) , (6, 84) , (7, 72) , (8, 63) , (9, 56) , (12, 42) , (14, 36) , (18, 28) and (21, 24)

How to find factors of a number in pair

Steps to find factors of 504 in pair

Example: Find factors of 504 in pair

Factor Pair Pair Factorization
1 and 504 1 x 504 = 504
2 and 252 2 x 252 = 504
3 and 168 3 x 168 = 504
4 and 126 4 x 126 = 504
6 and 84 6 x 84 = 504
7 and 72 7 x 72 = 504
8 and 63 8 x 63 = 504
9 and 56 9 x 56 = 504
12 and 42 12 x 42 = 504
14 and 36 14 x 36 = 504
18 and 28 18 x 28 = 504
21 and 24 21 x 24 = 504

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 504. They are called negative pair factors.

Hence, the negative pairs of 504 would be ( -1 , -504 ) .

What does factor pairs of a number mean?

Factor pairs are those factors in pair that can give original number when multiplied. Every natural number is a product of atleast one factor pair. Eg- 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. So, factors of 504 in pair are (1,504), (2,252), (3,168), (4,126), (6,84), (7,72), (8,63), (9,56), (12,42), (14,36), (18,28), (21,24).

How can we define factors?

In mathematics, a factor is a number which divides into another number exactly, without leaving any remainder. A factor of a number can be positive of negative.

Properties of Factors

  • Each number is a factor of itself. Eg. 504 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 504.
  • Every number is a factor of zero (0), since 504 x 0 = 0.
  • Every number other than 1 has at least two factors, namely the number itself and 1.
  • Every factor of a number is an exact divisor of that number, example 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 168, 252, 504 are exact divisors of 504.
  • 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. Each factor divides 504 without leaving a remainder.
  • Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 168, 252, 504 are all less than or equal to 504.

Steps to find Factors of 504

  • Step 1. Find all the numbers that would divide 504 without leaving any remainder. Starting with the number 1 upto 252 (half of 504). The number 1 and the number itself are always factors of the given number.
    504 ÷ 1 : Remainder = 0
    504 ÷ 2 : Remainder = 0
    504 ÷ 3 : Remainder = 0
    504 ÷ 4 : Remainder = 0
    504 ÷ 6 : Remainder = 0
    504 ÷ 7 : Remainder = 0
    504 ÷ 8 : Remainder = 0
    504 ÷ 9 : Remainder = 0
    504 ÷ 12 : Remainder = 0
    504 ÷ 14 : Remainder = 0
    504 ÷ 18 : Remainder = 0
    504 ÷ 21 : Remainder = 0
    504 ÷ 24 : Remainder = 0
    504 ÷ 28 : Remainder = 0
    504 ÷ 36 : Remainder = 0
    504 ÷ 42 : Remainder = 0
    504 ÷ 56 : Remainder = 0
    504 ÷ 63 : Remainder = 0
    504 ÷ 72 : Remainder = 0
    504 ÷ 84 : Remainder = 0
    504 ÷ 126 : Remainder = 0
    504 ÷ 168 : Remainder = 0
    504 ÷ 252 : Remainder = 0
    504 ÷ 504 : Remainder = 0

Hence, 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, and 504

Frequently Asked Questions

  • Is 504 a composite number?

    Yes 504 is a composite number.

  • Is 504 a prime number?

    No 504 is not a prime number.

  • What is the mean of factors of 504?

    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. therefore mean of factors of 504 is (1 + 2 + 3 + 4 + 6 + 7 + 8 + 9 + 12 + 14 + 18 + 21 + 24 + 28 + 36 + 42 + 56 + 63 + 72 + 84 + 126 + 168 + 252 + 504) / 24 = 65.00.

  • What do you mean by proper divisors?

    A number x is said to be the proper divisor of y if it divides y completely, given that x is smaller than y.

  • What do you mean by improper divisors?

    An improper divisor of a number is the number itself apart from this any divisor of a given number is a proper divisor.

Examples of Factors

Ariel has been asked to write all factor pairs of 504 but she is finding it difficult. Can you help her find out?

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. So, factors of 504 in pair are (1,504), (2,252), (3,168), (4,126), (6,84), (7,72), (8,63), (9,56), (12,42), (14,36), (18,28), (21,24).

Sammy wants to write all the negative factors of 504 in pair, but don't know how to start. Help Sammy in writing all the factor pairs.

Negative 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. Hence, factors of 504 in pair are (-1,-504), (-2,-252), (-3,-168), (-4,-126), (-6,-84), (-7,-72), (-8,-63), (-9,-56), (-12,-42), (-14,-36), (-18,-28), (-21,-24).

Help Deep in writing the positive factors of 504 in pair and negative factor of 504 in pair.

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. Positive factors of 504 in pair are (1,504), (2,252), (3,168), (4,126), (6,84), (7,72), (8,63), (9,56), (12,42), (14,36), (18,28), (21,24). Negative factors of 504 in pair are (-1,-504), (-2,-252), (-3,-168), (-4,-126), (-6,-84), (-7,-72), (-8,-63), (-9,-56), (-12,-42), (-14,-36), (-18,-28), (-21,-24).

Find the product of all factors of 504.

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. So the product of all factors of 504 would be 1 x 2 x 3 x 4 x 6 x 7 x 8 x 9 x 12 x 14 x 18 x 21 x 24 x 28 x 36 x 42 x 56 x 63 x 72 x 84 x 126 x 168 x 252 x 504 = 2.686373763955436e+32.

Find the product of all prime factors of 504.

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. Prime factors are 2, 2, 2, 3, 3, 7. So, the product of all prime factors of 504 would be 2 x 2 x 2 x 3 x 3 x 7 = 504.

Can you help Sammy list the factors of 504 and also find the factor pairs?

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.
Factors of 504 in pair are (1,504), (2,252), (3,168), (4,126), (6,84), (7,72), (8,63), (9,56), (12,42), (14,36), (18,28), (21,24).

Sammy has 504 blocks and he wants to arrange them in all possible ways to form a rectangle but he doesn't know the technique for doing that, help Sammy in arrangements.

To arrange 504 blocks in all possible ways to form a rectangle, we need to calculate factors of 504 in pair. Therefore, factors of 504 in pair are (1,504), (2,252), (3,168), (4,126), (6,84), (7,72), (8,63), (9,56), (12,42), (14,36), (18,28), (21,24)