# Factors of 828 in pair

Factors of 828 in pair are (1, 828) , (2, 414) , (3, 276) , (4, 207) , (6, 138) , (9, 92) , (12, 69) , (18, 46) and (23, 36)

#### How to find factors of a number in pair

 1.   Steps to find factors of 828 in pair 2.   What is factors of a number in pair? 3.   What are Factors? 4.   Frequently Asked Questions 5.   Examples of factors in pair

### Example: Find factors of 828 in pair

Factor Pair Pair Factorization
1 and 828 1 x 828 = 828
2 and 414 2 x 414 = 828
3 and 276 3 x 276 = 828
4 and 207 4 x 207 = 828
6 and 138 6 x 138 = 828
9 and 92 9 x 92 = 828
12 and 69 12 x 69 = 828
18 and 46 18 x 46 = 828
23 and 36 23 x 36 = 828

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 828. They are called negative pair factors.

Hence, the negative pairs of 828 would be ( -1 , -828 ) .

#### 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 828 are 1 , 2 , 3 , 4 , 6 , 9 , 12 , 18 , 23 , 36 , 46 , 69 , 92 , 138 , 207 , 276 , 414 , 828. So, factors of 828 in pair are (1,828), (2,414), (3,276), (4,207), (6,138), (9,92), (12,69), (18,46), (23,36).

#### 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. 828 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 828.
• Every number is a factor of zero (0), since 828 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, 23, 36, 46, 69, 92, 138, 207, 276, 414, 828 are exact divisors of 828.
• Factors of 828 are 1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 207, 276, 414, 828. Each factor divides 828 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, 23, 36, 46, 69, 92, 138, 207, 276, 414, 828 are all less than or equal to 828.

#### Steps to find Factors of 828

• Step 1. Find all the numbers that would divide 828 without leaving any remainder. Starting with the number 1 upto 414 (half of 828). The number 1 and the number itself are always factors of the given number.
828 ÷ 1 : Remainder = 0
828 ÷ 2 : Remainder = 0
828 ÷ 3 : Remainder = 0
828 ÷ 4 : Remainder = 0
828 ÷ 6 : Remainder = 0
828 ÷ 9 : Remainder = 0
828 ÷ 12 : Remainder = 0
828 ÷ 18 : Remainder = 0
828 ÷ 23 : Remainder = 0
828 ÷ 36 : Remainder = 0
828 ÷ 46 : Remainder = 0
828 ÷ 69 : Remainder = 0
828 ÷ 92 : Remainder = 0
828 ÷ 138 : Remainder = 0
828 ÷ 207 : Remainder = 0
828 ÷ 276 : Remainder = 0
828 ÷ 414 : Remainder = 0
828 ÷ 828 : Remainder = 0

Hence, Factors of 828 are 1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 207, 276, 414, and 828

• Is 828 a composite number?

Yes 828 is a composite number.

• Is 828 a prime number?

No 828 is not a prime number.

• What is the mean of factors of 828?

Factors of 828 are 1 , 2 , 3 , 4 , 6 , 9 , 12 , 18 , 23 , 36 , 46 , 69 , 92 , 138 , 207 , 276 , 414 , 828. therefore mean of factors of 828 is (1 + 2 + 3 + 4 + 6 + 9 + 12 + 18 + 23 + 36 + 46 + 69 + 92 + 138 + 207 + 276 + 414 + 828) / 18 = 121.33.

• 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 828.
- Writing all prime factors of 828.
- Writing all the possible factors of 828 in pair.
Help him in writing all these.

Positive factors of 828 are 1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 207, 276, 414, 828.
Prime factors of 828 are 2, 2, 3, 3, 23.
Factors of 828 in pair are (1,828), (2,414), (3,276), (4,207), (6,138), (9,92), (12,69), (18,46), (23,36).

What are the pair factors of 828?

Factors of 828 are 1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 207, 276, 414, 828. Hence, the factors of 828 in pair are (1,828), (2,414), (3,276), (4,207), (6,138), (9,92), (12,69), (18,46), (23,36).

Can you help Sammy list the factors of 828 and also find the factor pairs?

Factors of 828 are 1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 207, 276, 414, 828.
Factors of 828 in pair are (1,828), (2,414), (3,276), (4,207), (6,138), (9,92), (12,69), (18,46), (23,36).

The area of a rectangle is 828 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 828 in pair. So, the possible combinations (1,828), (2,414), (3,276), (4,207), (6,138), (9,92), (12,69), (18,46), (23,36).

Help Diji in finding factors of 828 by Prime Factorization method and then sorting factors of 828 in pairs.

Prime factorization of 828 is 2 x 2 x 3 x 3 x 23. Factors of 828 in pair can be written as (1,828), (2,414), (3,276), (4,207), (6,138), (9,92), (12,69), (18,46), (23,36).

Write the smallest prime factor of 828.

Smallest prime factor of 828 is 2.

Write the largest prime factor of 828.

Largest prime factor of 828 is 23.

Diji wants to write all the negative factors of 828. Can you help Diji in doing the same?

Negative factors of 828 are -1, -2, -3, -4, -6, -9, -12, -18, -23, -36, -46, -69, -92, -138, -207, -276, -414, -828.