# Factors of 231 in pair

Factors of 231 in pair are (1, 231) , (3, 77) , (7, 33) and (11, 21)

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

 1.   Steps to find factors of 231 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 231 in pair

Factor Pair Pair Factorization
1 and 231 1 x 231 = 231
3 and 77 3 x 77 = 231
7 and 33 7 x 33 = 231
11 and 21 11 x 21 = 231

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 231. They are called negative pair factors.

Hence, the negative pairs of 231 would be ( -1 , -231 ) .

#### Introduction to factor pairs

Factor pair in mathematics is defined as all factors of a given number which when written in pair and multiplied gives the original number. Every natural number is a product of atleast one factor pair. Eg- Factors of 231 are 1 , 3 , 7 , 11 , 21 , 33 , 77 , 231. So, factors of 231 in pair are (1,231), (3,77), (7,33), (11,21).

#### 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

• Every number is a factor of zero (0), since 231 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, 3, 7, 11, 21, 33, 77, 231 are exact divisors of 231.
• Factors of 231 are 1, 3, 7, 11, 21, 33, 77, 231. Each factor divides 231 without leaving a remainder.

#### Steps to find Factors of 231

• Step 1. Find all the numbers that would divide 231 without leaving any remainder. Starting with the number 1 upto 115 (half of 231). The number 1 and the number itself are always factors of the given number.
231 ÷ 1 : Remainder = 0
231 ÷ 3 : Remainder = 0
231 ÷ 7 : Remainder = 0
231 ÷ 11 : Remainder = 0
231 ÷ 21 : Remainder = 0
231 ÷ 33 : Remainder = 0
231 ÷ 77 : Remainder = 0
231 ÷ 231 : Remainder = 0

Hence, Factors of 231 are 1, 3, 7, 11, 21, 33, 77, and 231

• Is 231 a composite number?

Yes 231 is a composite number.

• Is 231 a perfect square?

No 231 is not a perfect square.

• Write all odd factors of 231?

The factors of 231 are 1, 3, 7, 11, 21, 33, 77, 231.
Odd factors of 231 are 1 , 3 , 7 , 11 , 21 , 33 , 77 , 231.

• What is the mean of all prime factors of 231?

Factors of 231 are 1 , 3 , 7 , 11 , 21 , 33 , 77 , 231. Prime factors of 231 are 3 , 7 , 11. Therefore mean of prime factors of 231 is (3 + 7 + 11) / 3 = 7.00.

• 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.

#### Examples of Factors

How many total number of factors of 231 in pair are possible?

Factors of 231 are 1, 3, 7, 11, 21, 33, 77, 231. Hence, the factors of 231 in pair are (1,231), (3,77), (7,33), (11,21). Therefore, in total 4 pairs of factors are possible.

Help Deep in writing the positive factors of 231 in pair and negative factor of 231 in pair.

Factors of 231 are 1, 3, 7, 11, 21, 33, 77, 231. Positive factors of 231 in pair are (1,231), (3,77), (7,33), (11,21). Negative factors of 231 in pair are (-1,-231), (-3,-77), (-7,-33), (-11,-21).

Find the product of all factors of 231.

Factors of 231 are 1, 3, 7, 11, 21, 33, 77, 231. So the product of all factors of 231 would be 1 x 3 x 7 x 11 x 21 x 33 x 77 x 231 = 2847396321.

Find the product of all prime factors of 231.

Factors of 231 are 1, 3, 7, 11, 21, 33, 77, 231. Prime factors are 3, 7, 11. So, the product of all prime factors of 231 would be 3 x 7 x 11 = 231.

A student has been assigned the following tasks by the teacher:
- Finding out all positive factors of 231.
- Writing all prime factors of 231.
- Writing all the possible factors of 231 in pair.
Help him in writing all these.

Positive factors of 231 are 1, 3, 7, 11, 21, 33, 77, 231.
Prime factors of 231 are 3, 7, 11.
Factors of 231 in pair are (1,231), (3,77), (7,33), (11,21).

What are the pair factors of 231?

Factors of 231 are 1, 3, 7, 11, 21, 33, 77, 231. Hence, the factors of 231 in pair are (1,231), (3,77), (7,33), (11,21).

Can you help Sammy list the factors of 231 and also find the factor pairs?

Factors of 231 are 1, 3, 7, 11, 21, 33, 77, 231.
Factors of 231 in pair are (1,231), (3,77), (7,33), (11,21).

Sammy has 231 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 231 blocks in all possible ways to form a rectangle, we need to calculate factors of 231 in pair. Therefore, factors of 231 in pair are (1,231), (3,77), (7,33), (11,21)