Factors of 408

2. Steps to find factors of 408 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 408 using the division method, follow these steps:

• Step 1. Start dividing 408 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 408, which is 2. Divide 408 by 2 to obtain the quotient (204).
  408 ÷ 2 = 204
• Step 3. Repeat step 1 with the obtained quotient (204).
  204 ÷ 2 = 102
  102 ÷ 2 = 51
  51 ÷ 3 = 17
  17 ÷ 17 = 1

So, the prime factorization of 408 is, 408 = 2 x 2 x 2 x 3 x 17.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 408 as shown below:

So, the prime factorization of 408 is, 408 = 2 x 2 x 2 x 3 x 17.

3. Find factors of 408 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 408 would be the two numbers which, when multiplied, give 408 as the result.

The following table represents the calculation of factors of 408 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 408. They are called negative pair factors.

Hence, the negative pairs of 408 would be ( -1 , -408 ) , ( -2 , -204 ) , ( -3 , -136 ) , ( -4 , -102 ) , ( -6 , -68 ) , ( -8 , -51 ) , ( -12 , -34 ) and ( -17 , -24 ) .

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. 408 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 408.
• Every number is a factor of zero (0), since 408 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, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408 are exact divisors of 408.
• Factors of 408 are 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408. Each factor divides 408 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408 are all less than or equal to 408.

Frequently Asked Questions

• What are the prime factors of 408?

  The factors of 408 are 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408.
  Prime factors of 408 are 2, 2, 2, 3, 17.

• What two numbers make 408?

  Two numbers that make 408 are 2 and 204.

• What is the greatest prime factors of 408?

  The greatest prime factor of 408 is 17.

• What are factors of 408?

  Factors of 408 are 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408.

• How do you find factors of a negative number? ( eg. -408 )?

  Factors of -408 are -1, -2, -3, -4, -6, -8, -12, -17, -24, -34, -51, -68, -102, -136, -204, -408.

• What are five multiples of 408?

  First five multiples of 408 are 816, 1224, 1632, 2040, 2448.

• Write some multiples of 408?

  First five multiples of 408 are 816, 1224, 1632, 2040.

• Is 408 a perfect square?

  No 408 is not a perfect square.

• What two numbers make 408?

  Two numbers that make 408 are 2 and 204.

Examples of Factors