# 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, and 504

#### How to find factors of a number

 1.   Find factors of 504 using Division Method 2.   Find factors of 504 using Prime Factorization 3.   Find factors of 504 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 504

• Divide 504 by 1: 504 ÷ 1 : Remainder = 0
• Divide 504 by 2: 504 ÷ 2 : Remainder = 0
• Divide 504 by 3: 504 ÷ 3 : Remainder = 0
• Divide 504 by 4: 504 ÷ 4 : Remainder = 0
• Divide 504 by 6: 504 ÷ 6 : Remainder = 0
• Divide 504 by 7: 504 ÷ 7 : Remainder = 0
• Divide 504 by 8: 504 ÷ 8 : Remainder = 0
• Divide 504 by 9: 504 ÷ 9 : Remainder = 0
• Divide 504 by 12: 504 ÷ 12 : Remainder = 0
• Divide 504 by 14: 504 ÷ 14 : Remainder = 0
• Divide 504 by 18: 504 ÷ 18 : Remainder = 0
• Divide 504 by 21: 504 ÷ 21 : Remainder = 0
• Divide 504 by 24: 504 ÷ 24 : Remainder = 0
• Divide 504 by 28: 504 ÷ 28 : Remainder = 0
• Divide 504 by 36: 504 ÷ 36 : Remainder = 0
• Divide 504 by 42: 504 ÷ 42 : Remainder = 0
• Divide 504 by 56: 504 ÷ 56 : Remainder = 0
• Divide 504 by 63: 504 ÷ 63 : Remainder = 0
• Divide 504 by 72: 504 ÷ 72 : Remainder = 0
• Divide 504 by 84: 504 ÷ 84 : Remainder = 0
• Divide 504 by 126: 504 ÷ 126 : Remainder = 0
• Divide 504 by 168: 504 ÷ 168 : Remainder = 0
• Divide 504 by 252: 504 ÷ 252 : Remainder = 0
• Divide 504 by 504: 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

#### 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:

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 ) , ( -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.

• 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

Ariel has been assigned the task to find the product of all the prime factors of 504. Can you help her?

Prime factors of 504 are 2, 2, 2, 3, 3, 7.
Hence, the product of prime factors of 42.

Can you help Rubel to find out the product of the even 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.
Even factors of 504 are 2, 4, 6, 8, 12, 14, 18, 24, 28, 36, 42, 56, 72, 84, 126, 168, 252, 504.
Hence, product of even factors of 504 is; 2 x 4 x 6 x 8 x 12 x 14 x 18 x 24 x 28 x 36 x 42 x 56 x 72 x 84 x 126 x 168 x 252 x 504 = 1.0743475282468638e+27.

Joy wants to calculate mean of all the factors of 504. Help him in finding the mean 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.
To calculate the mean we need to calculate the sum of factors first. Sum 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 = 1560.
Hence, the mean of factors of 504 is 1560 ÷ 24 = 65.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 504? Help her in writing all the factors.

Positive 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.
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.

How many factors are there for 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 there are in total 24 factors.

Joey wants to write all the prime factors of 504 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 504 are 2, 2, 2, 3, 3, 7.
So in exponential form it can be written as 23 x 32 x 7.

Kevin has been asked to write 23 factor(s) of 504. Can you predict the answer?

23 factor(s) 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.