Factors of 1512 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 27, 28, 36, 42, 54, 56, 63, 72, 84, 108, 126, 168, 189, 216, 252, 378, 504, 756, and 1512

How to find factors of a number

1. Steps to find factors of 1512 using Division Method

Example: Find factors of 1512

  • Divide 1512 by 1: 1512 ÷ 1 : Remainder = 0
  • Divide 1512 by 2: 1512 ÷ 2 : Remainder = 0
  • Divide 1512 by 3: 1512 ÷ 3 : Remainder = 0
  • Divide 1512 by 4: 1512 ÷ 4 : Remainder = 0
  • Divide 1512 by 6: 1512 ÷ 6 : Remainder = 0
  • Divide 1512 by 7: 1512 ÷ 7 : Remainder = 0
  • Divide 1512 by 8: 1512 ÷ 8 : Remainder = 0
  • Divide 1512 by 9: 1512 ÷ 9 : Remainder = 0
  • Divide 1512 by 12: 1512 ÷ 12 : Remainder = 0
  • Divide 1512 by 14: 1512 ÷ 14 : Remainder = 0
  • Divide 1512 by 18: 1512 ÷ 18 : Remainder = 0
  • Divide 1512 by 21: 1512 ÷ 21 : Remainder = 0
  • Divide 1512 by 24: 1512 ÷ 24 : Remainder = 0
  • Divide 1512 by 27: 1512 ÷ 27 : Remainder = 0
  • Divide 1512 by 28: 1512 ÷ 28 : Remainder = 0
  • Divide 1512 by 36: 1512 ÷ 36 : Remainder = 0
  • Divide 1512 by 42: 1512 ÷ 42 : Remainder = 0
  • Divide 1512 by 54: 1512 ÷ 54 : Remainder = 0
  • Divide 1512 by 56: 1512 ÷ 56 : Remainder = 0
  • Divide 1512 by 63: 1512 ÷ 63 : Remainder = 0
  • Divide 1512 by 72: 1512 ÷ 72 : Remainder = 0
  • Divide 1512 by 84: 1512 ÷ 84 : Remainder = 0
  • Divide 1512 by 108: 1512 ÷ 108 : Remainder = 0
  • Divide 1512 by 126: 1512 ÷ 126 : Remainder = 0
  • Divide 1512 by 168: 1512 ÷ 168 : Remainder = 0
  • Divide 1512 by 189: 1512 ÷ 189 : Remainder = 0
  • Divide 1512 by 216: 1512 ÷ 216 : Remainder = 0
  • Divide 1512 by 252: 1512 ÷ 252 : Remainder = 0
  • Divide 1512 by 378: 1512 ÷ 378 : Remainder = 0
  • Divide 1512 by 504: 1512 ÷ 504 : Remainder = 0
  • Divide 1512 by 756: 1512 ÷ 756 : Remainder = 0
  • Divide 1512 by 1512: 1512 ÷ 1512 : Remainder = 0

Hence, Factors of 1512 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 27, 28, 36, 42, 54, 56, 63, 72, 84, 108, 126, 168, 189, 216, 252, 378, 504, 756, and 1512

2. Steps to find factors of 1512 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 1512 using the division method, follow these steps:

  • Step 1. Start dividing 1512 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 1512, which is 2. Divide 1512 by 2 to obtain the quotient (756).
    1512 ÷ 2 = 756
  • Step 3. Repeat step 1 with the obtained quotient (756).
    756 ÷ 2 = 378
    378 ÷ 2 = 189
    189 ÷ 3 = 63
    63 ÷ 3 = 21
    21 ÷ 3 = 7
    7 ÷ 7 = 1

So, the prime factorization of 1512 is, 1512 = 2 x 2 x 2 x 3 x 3 x 3 x 7.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 1512 as shown below:

So, the prime factorization of 1512 is, 1512 = 2 x 2 x 2 x 3 x 3 x 3 x 7.

3. Find factors of 1512 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 1512 would be the two numbers which, when multiplied, give 1512 as the result.

The following table represents the calculation of factors of 1512 in pairs:

Factor Pair Pair Factorization
1 and 1512 1 x 1512 = 1512
2 and 756 2 x 756 = 1512
3 and 504 3 x 504 = 1512
4 and 378 4 x 378 = 1512
6 and 252 6 x 252 = 1512
7 and 216 7 x 216 = 1512
8 and 189 8 x 189 = 1512
9 and 168 9 x 168 = 1512
12 and 126 12 x 126 = 1512
14 and 108 14 x 108 = 1512
18 and 84 18 x 84 = 1512
21 and 72 21 x 72 = 1512
24 and 63 24 x 63 = 1512
27 and 56 27 x 56 = 1512
28 and 54 28 x 54 = 1512
36 and 42 36 x 42 = 1512

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 1512. They are called negative pair factors.

Hence, the negative pairs of 1512 would be ( -1 , -1512 ) , ( -2 , -756 ) , ( -3 , -504 ) , ( -4 , -378 ) , ( -6 , -252 ) , ( -7 , -216 ) , ( -8 , -189 ) , ( -9 , -168 ) , ( -12 , -126 ) , ( -14 , -108 ) , ( -18 , -84 ) , ( -21 , -72 ) , ( -24 , -63 ) , ( -27 , -56 ) , ( -28 , -54 ) and ( -36 , -42 ) .

How do you explain factors?

In mathematics, a factor is a number or also it can be an algebraic expression that divides another number or any expression completely and that too without leaving any remainder. A factor of a number can be positive or negative.

Properties of factors

  • Each number is a factor of itself. Eg. 1512 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 1512.
  • Every number is a factor of zero (0), since 1512 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, 27, 28, 36, 42, 54, 56, 63, 72, 84, 108, 126, 168, 189, 216, 252, 378, 504, 756, 1512 are exact divisors of 1512.
  • Factors of 1512 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 27, 28, 36, 42, 54, 56, 63, 72, 84, 108, 126, 168, 189, 216, 252, 378, 504, 756, 1512. Each factor divides 1512 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, 27, 28, 36, 42, 54, 56, 63, 72, 84, 108, 126, 168, 189, 216, 252, 378, 504, 756, 1512 are all less than or equal to 1512.

Frequently Asked Questions

  • Which is the smallest prime factor of 1512?

    Smallest prime factor of 1512 is 2.

  • Is 1512 a perfect square?

    No 1512 is not a perfect square.

  • What are five multiples of 1512?

    First five multiples of 1512 are 3024, 4536, 6048, 7560, 9072.

  • What is prime factorization of 1512?

    Prime factorization of 1512 is 2 x 2 x 2 x 3 x 3 x 3 x 7.

  • What are factors of 1512?

    Factors of 1512 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 27, 28, 36, 42, 54, 56, 63, 72, 84, 108, 126, 168, 189, 216, 252, 378, 504, 756, 1512.

  • How do you find factors of a negative number? ( eg. -1512 )?

    Factors of -1512 are -1, -2, -3, -4, -6, -7, -8, -9, -12, -14, -18, -21, -24, -27, -28, -36, -42, -54, -56, -63, -72, -84, -108, -126, -168, -189, -216, -252, -378, -504, -756, -1512.

  • Is 1512 a whole number?

    Yes 1512 is a whole number.

  • Which is greatest factor of 1512?

    The greatest factor of 1512 is 756.

  • What are the prime factors of 1512?

    The factors of 1512 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 27, 28, 36, 42, 54, 56, 63, 72, 84, 108, 126, 168, 189, 216, 252, 378, 504, 756, 1512.
    Prime factors of 1512 are 2, 2, 2, 3, 3, 3, 7.

Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 1512. Can you help her?

Prime factors of 1512 are 2, 2, 2, 3, 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 1512?

Factors of 1512 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 27, 28, 36, 42, 54, 56, 63, 72, 84, 108, 126, 168, 189, 216, 252, 378, 504, 756, 1512.
Even factors of 1512 are 2, 4, 6, 8, 12, 14, 18, 24, 28, 36, 42, 54, 56, 72, 84, 108, 126, 168, 216, 252, 378, 504, 756, 1512.
Hence, product of even factors of 1512 is; 2 x 4 x 6 x 8 x 12 x 14 x 18 x 24 x 28 x 36 x 42 x 54 x 56 x 72 x 84 x 108 x 126 x 168 x 216 x 252 x 378 x 504 x 756 x 1512 = 5.847650957272025e+41.

Joy wants to calculate mean of all the factors of 1512. Help him in finding the mean of 1512.

Factors of 1512 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 27, 28, 36, 42, 54, 56, 63, 72, 84, 108, 126, 168, 189, 216, 252, 378, 504, 756, 1512.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 1512 is 1 + 2 + 3 + 4 + 6 + 7 + 8 + 9 + 12 + 14 + 18 + 21 + 24 + 27 + 28 + 36 + 42 + 54 + 56 + 63 + 72 + 84 + 108 + 126 + 168 + 189 + 216 + 252 + 378 + 504 + 756 + 1512 = 4800.
Hence, the mean of factors of 1512 is 4800 ÷ 32 = 150.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 1512? Help her in writing all the factors.

Positive factors are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 27, 28, 36, 42, 54, 56, 63, 72, 84, 108, 126, 168, 189, 216, 252, 378, 504, 756, 1512.
Negative factors are -1, -2, -3, -4, -6, -7, -8, -9, -12, -14, -18, -21, -24, -27, -28, -36, -42, -54, -56, -63, -72, -84, -108, -126, -168, -189, -216, -252, -378, -504, -756, -1512.

How many factors are there for 1512?

Factors of 1512 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 27, 28, 36, 42, 54, 56, 63, 72, 84, 108, 126, 168, 189, 216, 252, 378, 504, 756, 1512.
So there are in total 32 factors.

Joey wants to write all the prime factors of 1512 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 1512 are 2, 2, 2, 3, 3, 3, 7.
So in exponential form it can be written as 23 x 33 x 7.

Kevin has been asked to write 31 factor(s) of 1512. Can you predict the answer?

31 factor(s) of 1512 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 27, 28, 36, 42, 54, 56, 63, 72, 84, 108, 126, 168, 189, 216, 252, 378, 504, 756.