Factors of 504

2. Steps to find factors of 504 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

Method 1: Division Method

To find the primefactors of 504 using the division method, follow these steps:

• Step 1. Start dividing 504 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
• Step 2. After finding the smallest prime factor of the number 504, which is 2. Divide 504 by 2 to obtain the quotient (252).
  504 ÷ 2 = 252
• Step 3. Repeat step 1 with the obtained quotient (252).
  252 ÷ 2 = 126
  126 ÷ 2 = 63
  63 ÷ 3 = 21
  21 ÷ 3 = 7
  7 ÷ 7 = 1

So, the prime factorization of 504 is, 504 = 2 x 2 x 2 x 3 x 3 x 7.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 504 as shown below:

So, the prime factorization of 504 is, 504 = 2 x 2 x 2 x 3 x 3 x 7.

3. Find factors of 504 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 504 would be the two numbers which, when multiplied, give 504 as the result.

The following table represents the calculation of factors of 504 in pairs:

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 ) , ( -2 , -252 ) , ( -3 , -168 ) , ( -4 , -126 ) , ( -6 , -84 ) , ( -7 , -72 ) , ( -8 , -63 ) , ( -9 , -56 ) , ( -12 , -42 ) , ( -14 , -36 ) , ( -18 , -28 ) and ( -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.

Frequently Asked Questions

• Which is the smallest prime factor of 504?

  Smallest prime factor of 504 is 2.

• Is 504 a perfect square?

  No 504 is not a perfect square.

• What are five multiples of 504?

  First five multiples of 504 are 1008, 1512, 2016, 2520, 3024.

• What is prime factorization of 504?

  Prime factorization of 504 is 2 x 2 x 2 x 3 x 3 x 7.

• What are 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.

• How do you find factors of a negative number? ( eg. -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.

• Is 504 a whole number?

  Yes 504 is a whole number.

• Which is greatest factor of 504?

  The greatest factor of 504 is 252.

• What are the prime 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.
  Prime factors of 504 are 2, 2, 2, 3, 3, 7.

Examples of Factors