Factors of 1008 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 36, 42, 48, 56, 63, 72, 84, 112, 126, 144, 168, 252, 336, 504, and 1008

How to find factors of a number

1. Steps to find factors of 1008 using Division Method

Example: Find factors of 1008

  • Divide 1008 by 1: 1008 ÷ 1 : Remainder = 0
  • Divide 1008 by 2: 1008 ÷ 2 : Remainder = 0
  • Divide 1008 by 3: 1008 ÷ 3 : Remainder = 0
  • Divide 1008 by 4: 1008 ÷ 4 : Remainder = 0
  • Divide 1008 by 6: 1008 ÷ 6 : Remainder = 0
  • Divide 1008 by 7: 1008 ÷ 7 : Remainder = 0
  • Divide 1008 by 8: 1008 ÷ 8 : Remainder = 0
  • Divide 1008 by 9: 1008 ÷ 9 : Remainder = 0
  • Divide 1008 by 12: 1008 ÷ 12 : Remainder = 0
  • Divide 1008 by 14: 1008 ÷ 14 : Remainder = 0
  • Divide 1008 by 16: 1008 ÷ 16 : Remainder = 0
  • Divide 1008 by 18: 1008 ÷ 18 : Remainder = 0
  • Divide 1008 by 21: 1008 ÷ 21 : Remainder = 0
  • Divide 1008 by 24: 1008 ÷ 24 : Remainder = 0
  • Divide 1008 by 28: 1008 ÷ 28 : Remainder = 0
  • Divide 1008 by 36: 1008 ÷ 36 : Remainder = 0
  • Divide 1008 by 42: 1008 ÷ 42 : Remainder = 0
  • Divide 1008 by 48: 1008 ÷ 48 : Remainder = 0
  • Divide 1008 by 56: 1008 ÷ 56 : Remainder = 0
  • Divide 1008 by 63: 1008 ÷ 63 : Remainder = 0
  • Divide 1008 by 72: 1008 ÷ 72 : Remainder = 0
  • Divide 1008 by 84: 1008 ÷ 84 : Remainder = 0
  • Divide 1008 by 112: 1008 ÷ 112 : Remainder = 0
  • Divide 1008 by 126: 1008 ÷ 126 : Remainder = 0
  • Divide 1008 by 144: 1008 ÷ 144 : Remainder = 0
  • Divide 1008 by 168: 1008 ÷ 168 : Remainder = 0
  • Divide 1008 by 252: 1008 ÷ 252 : Remainder = 0
  • Divide 1008 by 336: 1008 ÷ 336 : Remainder = 0
  • Divide 1008 by 504: 1008 ÷ 504 : Remainder = 0
  • Divide 1008 by 1008: 1008 ÷ 1008 : Remainder = 0

Hence, Factors of 1008 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 36, 42, 48, 56, 63, 72, 84, 112, 126, 144, 168, 252, 336, 504, and 1008

2. Steps to find factors of 1008 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 1008 using the division method, follow these steps:

  • Step 1. Start dividing 1008 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 1008, which is 2. Divide 1008 by 2 to obtain the quotient (504).
    1008 ÷ 2 = 504
  • Step 3. Repeat step 1 with the obtained quotient (504).
    504 ÷ 2 = 252
    252 ÷ 2 = 126
    126 ÷ 2 = 63
    63 ÷ 3 = 21
    21 ÷ 3 = 7
    7 ÷ 7 = 1

So, the prime factorization of 1008 is, 1008 = 2 x 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 1008 as shown below:

So, the prime factorization of 1008 is, 1008 = 2 x 2 x 2 x 2 x 3 x 3 x 7.

3. Find factors of 1008 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 1008 would be the two numbers which, when multiplied, give 1008 as the result.

The following table represents the calculation of factors of 1008 in pairs:

Factor Pair Pair Factorization
1 and 1008 1 x 1008 = 1008
2 and 504 2 x 504 = 1008
3 and 336 3 x 336 = 1008
4 and 252 4 x 252 = 1008
6 and 168 6 x 168 = 1008
7 and 144 7 x 144 = 1008
8 and 126 8 x 126 = 1008
9 and 112 9 x 112 = 1008
12 and 84 12 x 84 = 1008
14 and 72 14 x 72 = 1008
16 and 63 16 x 63 = 1008
18 and 56 18 x 56 = 1008
21 and 48 21 x 48 = 1008
24 and 42 24 x 42 = 1008
28 and 36 28 x 36 = 1008

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 1008. They are called negative pair factors.

Hence, the negative pairs of 1008 would be ( -1 , -1008 ) , ( -2 , -504 ) , ( -3 , -336 ) , ( -4 , -252 ) , ( -6 , -168 ) , ( -7 , -144 ) , ( -8 , -126 ) , ( -9 , -112 ) , ( -12 , -84 ) , ( -14 , -72 ) , ( -16 , -63 ) , ( -18 , -56 ) , ( -21 , -48 ) , ( -24 , -42 ) and ( -28 , -36 ) .

What is the definition of factors?

In mathematics, factors are number, algebraic expressions which when multiplied together produce desired product. A factor of a number can be positive or negative.

Properties of factors

  • Each number is a factor of itself. Eg. 1008 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 1008.
  • Every number is a factor of zero (0), since 1008 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, 16, 18, 21, 24, 28, 36, 42, 48, 56, 63, 72, 84, 112, 126, 144, 168, 252, 336, 504, 1008 are exact divisors of 1008.
  • Factors of 1008 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 36, 42, 48, 56, 63, 72, 84, 112, 126, 144, 168, 252, 336, 504, 1008. Each factor divides 1008 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, 16, 18, 21, 24, 28, 36, 42, 48, 56, 63, 72, 84, 112, 126, 144, 168, 252, 336, 504, 1008 are all less than or equal to 1008.

Frequently Asked Questions

  • Which is the smallest prime factor of 1008?

    Smallest prime factor of 1008 is 2.

  • Is 1008 a perfect square?

    No 1008 is not a perfect square.

  • What are five multiples of 1008?

    First five multiples of 1008 are 2016, 3024, 4032, 5040, 6048.

  • What is prime factorization of 1008?

    Prime factorization of 1008 is 2 x 2 x 2 x 2 x 3 x 3 x 7.

  • What are factors of 1008?

    Factors of 1008 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 36, 42, 48, 56, 63, 72, 84, 112, 126, 144, 168, 252, 336, 504, 1008.

  • How do you find factors of a negative number? ( eg. -1008 )?

    Factors of -1008 are -1, -2, -3, -4, -6, -7, -8, -9, -12, -14, -16, -18, -21, -24, -28, -36, -42, -48, -56, -63, -72, -84, -112, -126, -144, -168, -252, -336, -504, -1008.

  • Is 1008 a whole number?

    Yes 1008 is a whole number.

  • Which is greatest factor of 1008?

    The greatest factor of 1008 is 504.

  • What are the prime factors of 1008?

    The factors of 1008 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 36, 42, 48, 56, 63, 72, 84, 112, 126, 144, 168, 252, 336, 504, 1008.
    Prime factors of 1008 are 2, 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 1008. Can you help her?

Prime factors of 1008 are 2, 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 1008?

Factors of 1008 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 36, 42, 48, 56, 63, 72, 84, 112, 126, 144, 168, 252, 336, 504, 1008.
Even factors of 1008 are 2, 4, 6, 8, 12, 14, 16, 18, 24, 28, 36, 42, 48, 56, 72, 84, 112, 126, 144, 168, 252, 336, 504, 1008.
Hence, product of even factors of 1008 is; 2 x 4 x 6 x 8 x 12 x 14 x 16 x 18 x 24 x 28 x 36 x 42 x 48 x 56 x 72 x 84 x 112 x 126 x 144 x 168 x 252 x 336 x 504 x 1008 = 4.506987289461336e+39.

Joy wants to calculate mean of all the factors of 1008. Help him in finding the mean of 1008.

Factors of 1008 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 36, 42, 48, 56, 63, 72, 84, 112, 126, 144, 168, 252, 336, 504, 1008.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 1008 is 1 + 2 + 3 + 4 + 6 + 7 + 8 + 9 + 12 + 14 + 16 + 18 + 21 + 24 + 28 + 36 + 42 + 48 + 56 + 63 + 72 + 84 + 112 + 126 + 144 + 168 + 252 + 336 + 504 + 1008 = 3224.
Hence, the mean of factors of 1008 is 3224 ÷ 30 = 107.47.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 1008? Help her in writing all the factors.

Positive factors are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 36, 42, 48, 56, 63, 72, 84, 112, 126, 144, 168, 252, 336, 504, 1008.
Negative factors are -1, -2, -3, -4, -6, -7, -8, -9, -12, -14, -16, -18, -21, -24, -28, -36, -42, -48, -56, -63, -72, -84, -112, -126, -144, -168, -252, -336, -504, -1008.

How many factors are there for 1008?

Factors of 1008 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 36, 42, 48, 56, 63, 72, 84, 112, 126, 144, 168, 252, 336, 504, 1008.
So there are in total 30 factors.

Joey wants to write all the prime factors of 1008 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 1008 are 2, 2, 2, 2, 3, 3, 7.
So in exponential form it can be written as 24 x 32 x 7.

Kevin has been asked to write 29 factor(s) of 1008. Can you predict the answer?

29 factor(s) of 1008 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 36, 42, 48, 56, 63, 72, 84, 112, 126, 144, 168, 252, 336, 504.