Factors of 408 in pair are (1, 408) , (2, 204) , (3, 136) , (4, 102) , (6, 68) , (8, 51) , (12, 34) and (17, 24)

How to find factors of a number in pair

Steps to find factors of 408 in pair

Example: Find factors of 408 in pair

Factor Pair Pair Factorization
1 and 408 1 x 408 = 408
2 and 204 2 x 204 = 408
3 and 136 3 x 136 = 408
4 and 102 4 x 102 = 408
6 and 68 6 x 68 = 408
8 and 51 8 x 51 = 408
12 and 34 12 x 34 = 408
17 and 24 17 x 24 = 408

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 ) .

What does factor pairs in mathematics mean?

In mathematics, factor pair of a number are all those possible combination which when multiplied together give the original number in return. Every natural number is a product of atleast one factor pair. Eg- Factors of 408 are 1 , 2 , 3 , 4 , 6 , 8 , 12 , 17 , 24 , 34 , 51 , 68 , 102 , 136 , 204 , 408. So, factors of 408 in pair are (1,408), (2,204), (3,136), (4,102), (6,68), (8,51), (12,34), (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.

Steps to find Factors of 408

  • Step 1. Find all the numbers that would divide 408 without leaving any remainder. Starting with the number 1 upto 204 (half of 408). The number 1 and the number itself are always factors of the given number.
    408 ÷ 1 : Remainder = 0
    408 ÷ 2 : Remainder = 0
    408 ÷ 3 : Remainder = 0
    408 ÷ 4 : Remainder = 0
    408 ÷ 6 : Remainder = 0
    408 ÷ 8 : Remainder = 0
    408 ÷ 12 : Remainder = 0
    408 ÷ 17 : Remainder = 0
    408 ÷ 24 : Remainder = 0
    408 ÷ 34 : Remainder = 0
    408 ÷ 51 : Remainder = 0
    408 ÷ 68 : Remainder = 0
    408 ÷ 102 : Remainder = 0
    408 ÷ 136 : Remainder = 0
    408 ÷ 204 : Remainder = 0
    408 ÷ 408 : Remainder = 0

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

Frequently Asked Questions

  • Is 408 a composite number?

    Yes 408 is a composite number.

  • Is 408 a prime number?

    No 408 is not a prime number.

  • What is the mean of factors of 408?

    Factors of 408 are 1 , 2 , 3 , 4 , 6 , 8 , 12 , 17 , 24 , 34 , 51 , 68 , 102 , 136 , 204 , 408. therefore mean of factors of 408 is (1 + 2 + 3 + 4 + 6 + 8 + 12 + 17 + 24 + 34 + 51 + 68 + 102 + 136 + 204 + 408) / 16 = 67.50.

  • What do you mean by proper divisors?

    A number x is said to be the proper divisor of y if it divides y completely, given that x is smaller than y.

  • What do you mean by improper divisors?

    An improper divisor of a number is the number itself apart from this any divisor of a given number is a proper divisor.

Examples of Factors

Ariel has been asked to write all factor pairs of 408 but she is finding it difficult. Can you help her find out?

Factors of 408 are 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408. So, factors of 408 in pair are (1,408), (2,204), (3,136), (4,102), (6,68), (8,51), (12,34), (17,24).

Sammy wants to write all the negative factors of 408 in pair, but don't know how to start. Help Sammy in writing all the factor pairs.

Negative factors of 408 are -1, -2, -3, -4, -6, -8, -12, -17, -24, -34, -51, -68, -102, -136, -204, -408. Hence, factors of 408 in pair are (-1,-408), (-2,-204), (-3,-136), (-4,-102), (-6,-68), (-8,-51), (-12,-34), (-17,-24).

Help Deep in writing the positive factors of 408 in pair and negative factor of 408 in pair.

Factors of 408 are 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408. Positive factors of 408 in pair are (1,408), (2,204), (3,136), (4,102), (6,68), (8,51), (12,34), (17,24). Negative factors of 408 in pair are (-1,-408), (-2,-204), (-3,-136), (-4,-102), (-6,-68), (-8,-51), (-12,-34), (-17,-24).

Find the product of all factors of 408.

Factors of 408 are 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408. So the product of all factors of 408 would be 1 x 2 x 3 x 4 x 6 x 8 x 12 x 17 x 24 x 34 x 51 x 68 x 102 x 136 x 204 x 408 = 767858691933644800000.

Find the product of all prime factors of 408.

Factors of 408 are 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408. Prime factors are 2, 2, 2, 3, 17. So, the product of all prime factors of 408 would be 2 x 2 x 2 x 3 x 17 = 408.

Can you help Sammy list the factors of 408 and also find the factor pairs?

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

Sammy has 408 blocks and he wants to arrange them in all possible ways to form a rectangle but he doesn't know the technique for doing that, help Sammy in arrangements.

To arrange 408 blocks in all possible ways to form a rectangle, we need to calculate factors of 408 in pair. Therefore, factors of 408 in pair are (1,408), (2,204), (3,136), (4,102), (6,68), (8,51), (12,34), (17,24)