Factors of 684 in pair are (1, 684) , (2, 342) , (3, 228) , (4, 171) , (6, 114) , (9, 76) , (12, 57) , (18, 38) and (19, 36)

How to find factors of a number in pair

Steps to find factors of 684 in pair

Example: Find factors of 684 in pair

Factor Pair Pair Factorization
1 and 684 1 x 684 = 684
2 and 342 2 x 342 = 684
3 and 228 3 x 228 = 684
4 and 171 4 x 171 = 684
6 and 114 6 x 114 = 684
9 and 76 9 x 76 = 684
12 and 57 12 x 57 = 684
18 and 38 18 x 38 = 684
19 and 36 19 x 36 = 684

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 684. They are called negative pair factors.

Hence, the negative pairs of 684 would be ( -1 , -684 ) .

What does factor pairs of a number mean?

Factor pairs are those factors in pair that can give original number when multiplied. Every natural number is a product of atleast one factor pair. Eg- Factors of 684 are 1 , 2 , 3 , 4 , 6 , 9 , 12 , 18 , 19 , 36 , 38 , 57 , 76 , 114 , 171 , 228 , 342 , 684. So, factors of 684 in pair are (1,684), (2,342), (3,228), (4,171), (6,114), (9,76), (12,57), (18,38), (19,36).

How can we define factors?

In mathematics, a factor is a number which divides into another number exactly, without leaving any remainder. A factor of a number can be positive of negative.

Properties of Factors

  • Each number is a factor of itself. Eg. 684 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 684.
  • Every number is a factor of zero (0), since 684 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, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, 342, 684 are exact divisors of 684.
  • Factors of 684 are 1, 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, 342, 684. Each factor divides 684 without leaving a remainder.
  • Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, 342, 684 are all less than or equal to 684.

Steps to find Factors of 684

  • Step 1. Find all the numbers that would divide 684 without leaving any remainder. Starting with the number 1 upto 342 (half of 684). The number 1 and the number itself are always factors of the given number.
    684 ÷ 1 : Remainder = 0
    684 ÷ 2 : Remainder = 0
    684 ÷ 3 : Remainder = 0
    684 ÷ 4 : Remainder = 0
    684 ÷ 6 : Remainder = 0
    684 ÷ 9 : Remainder = 0
    684 ÷ 12 : Remainder = 0
    684 ÷ 18 : Remainder = 0
    684 ÷ 19 : Remainder = 0
    684 ÷ 36 : Remainder = 0
    684 ÷ 38 : Remainder = 0
    684 ÷ 57 : Remainder = 0
    684 ÷ 76 : Remainder = 0
    684 ÷ 114 : Remainder = 0
    684 ÷ 171 : Remainder = 0
    684 ÷ 228 : Remainder = 0
    684 ÷ 342 : Remainder = 0
    684 ÷ 684 : Remainder = 0

Hence, Factors of 684 are 1, 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, 342, and 684

Frequently Asked Questions

  • Is 684 a composite number?

    Yes 684 is a composite number.

  • Is 684 a prime number?

    No 684 is not a prime number.

  • What is the mean of factors of 684?

    Factors of 684 are 1 , 2 , 3 , 4 , 6 , 9 , 12 , 18 , 19 , 36 , 38 , 57 , 76 , 114 , 171 , 228 , 342 , 684. therefore mean of factors of 684 is (1 + 2 + 3 + 4 + 6 + 9 + 12 + 18 + 19 + 36 + 38 + 57 + 76 + 114 + 171 + 228 + 342 + 684) / 18 = 101.11.

  • 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

Rustom has been assigned the following tasks by the teacher:
- Finding out all positive factors of 684.
- Writing all prime factors of 684.
- Writing all the possible factors of 684 in pair.
Help him in writing all these.

Positive factors of 684 are 1, 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, 342, 684.
Prime factors of 684 are 2, 2, 3, 3, 19.
Factors of 684 in pair are (1,684), (2,342), (3,228), (4,171), (6,114), (9,76), (12,57), (18,38), (19,36).

What are the pair factors of 684?

Factors of 684 are 1, 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, 342, 684. Hence, the factors of 684 in pair are (1,684), (2,342), (3,228), (4,171), (6,114), (9,76), (12,57), (18,38), (19,36).

Can you help Sammy list the factors of 684 and also find the factor pairs?

Factors of 684 are 1, 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, 342, 684.
Factors of 684 in pair are (1,684), (2,342), (3,228), (4,171), (6,114), (9,76), (12,57), (18,38), (19,36).

The area of a rectangle is 684 square meters. List all the possible combinations possible for length and breadth in which a designer can design out all the combinations.

For the possible combinations possible for length and breadth in which a designer can design out all the rectangles can be calculated by calculating the factors of 684 in pair. So, the possible combinations (1,684), (2,342), (3,228), (4,171), (6,114), (9,76), (12,57), (18,38), (19,36).

Help Diji in finding factors of 684 by Prime Factorization method and then sorting factors of 684 in pairs.

Prime factorization of 684 is 2 x 2 x 3 x 3 x 19. Factors of 684 in pair can be written as (1,684), (2,342), (3,228), (4,171), (6,114), (9,76), (12,57), (18,38), (19,36).

Write the smallest prime factor of 684.

Smallest prime factor of 684 is 2.

Write the largest prime factor of 684.

Largest prime factor of 684 is 19.

Diji wants to write all the negative factors of 684. Can you help Diji in doing the same?

Negative factors of 684 are -1, -2, -3, -4, -6, -9, -12, -18, -19, -36, -38, -57, -76, -114, -171, -228, -342, -684.