Factors of 756

2. Steps to find factors of 756 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 756 using the division method, follow these steps:

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

So, the prime factorization of 756 is, 756 = 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 756 as shown below:

So, the prime factorization of 756 is, 756 = 2 x 2 x 3 x 3 x 3 x 7.

3. Find factors of 756 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 756 would be the two numbers which, when multiplied, give 756 as the result.

The following table represents the calculation of factors of 756 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 756. They are called negative pair factors.

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

How can we define factors?

In mathematics a factor is a number which divides into another without leaving any remainder. Or we can say, any two numbers that multiply to give a product are both factors of that product. It can be both positive or negative.

Properties of factors

• Each number is a factor of itself. Eg. 756 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 756.
• Every number is a factor of zero (0), since 756 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, 9, 12, 14, 18, 21, 27, 28, 36, 42, 54, 63, 84, 108, 126, 189, 252, 378, 756 are exact divisors of 756.
• Factors of 756 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 27, 28, 36, 42, 54, 63, 84, 108, 126, 189, 252, 378, 756. Each factor divides 756 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 27, 28, 36, 42, 54, 63, 84, 108, 126, 189, 252, 378, 756 are all less than or equal to 756.

Frequently Asked Questions

• Which is the smallest prime factor of 756?

  Smallest prime factor of 756 is 2.

• Is 756 a perfect square?

  No 756 is not a perfect square.

• What are five multiples of 756?

  First five multiples of 756 are 1512, 2268, 3024, 3780, 4536.

• What is prime factorization of 756?

  Prime factorization of 756 is 2 x 2 x 3 x 3 x 3 x 7.

• What are factors of 756?

  Factors of 756 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 27, 28, 36, 42, 54, 63, 84, 108, 126, 189, 252, 378, 756.

• How do you find factors of a negative number? ( eg. -756 )?

  Factors of -756 are -1, -2, -3, -4, -6, -7, -9, -12, -14, -18, -21, -27, -28, -36, -42, -54, -63, -84, -108, -126, -189, -252, -378, -756.

• Is 756 a whole number?

  Yes 756 is a whole number.

• Which is greatest factor of 756?

  The greatest factor of 756 is 378.

• What are the prime factors of 756?

  The factors of 756 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 27, 28, 36, 42, 54, 63, 84, 108, 126, 189, 252, 378, 756.
  Prime factors of 756 are 2, 2, 3, 3, 3, 7.

Examples of Factors