# Factors of 441 in pair

Factors of 441 in pair are (1, 441) , (3, 147) , (7, 63) , (9, 49) and (21, 21)

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

 1.   Steps to find factors of 441 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 441 in pair

Factor Pair Pair Factorization
1 and 441 1 x 441 = 441
3 and 147 3 x 147 = 441
7 and 63 7 x 63 = 441
9 and 49 9 x 49 = 441
21 and 21 21 x 21 = 441

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 441. They are called negative pair factors.

Hence, the negative pairs of 441 would be ( -1 , -441 ) .

#### 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 441 are 1 , 3 , 7 , 9 , 21 , 49 , 63 , 147 , 441. So, factors of 441 in pair are (1,441), (3,147), (7,63), (9,49), (21,21).

#### 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 factor of a number is an exact divisor of that number, example 1, 3, 7, 9, 21, 49, 63, 147, 441 are exact divisors of 441.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Each number is a factor of itself. Eg. 441 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 441.

#### Steps to find Factors of 441

• Step 1. Find all the numbers that would divide 441 without leaving any remainder. Starting with the number 1 upto 220 (half of 441). The number 1 and the number itself are always factors of the given number.
441 ÷ 1 : Remainder = 0
441 ÷ 3 : Remainder = 0
441 ÷ 7 : Remainder = 0
441 ÷ 9 : Remainder = 0
441 ÷ 21 : Remainder = 0
441 ÷ 49 : Remainder = 0
441 ÷ 63 : Remainder = 0
441 ÷ 147 : Remainder = 0
441 ÷ 441 : Remainder = 0

Hence, Factors of 441 are 1, 3, 7, 9, 21, 49, 63, 147, and 441

• Is 441 a composite number?

Yes 441 is a composite number.

• Is 441 a perfect square?

Yes 441 is a perfect square.

• Write all odd factors of 441?

The factors of 441 are 1, 3, 7, 9, 21, 49, 63, 147, 441.
Odd factors of 441 are 1 , 3 , 7 , 9 , 21 , 49 , 63 , 147 , 441.

• What is the mean of all prime factors of 441?

Factors of 441 are 1 , 3 , 7 , 9 , 21 , 49 , 63 , 147 , 441. Prime factors of 441 are 3 , 3 , 7 , 7. Therefore mean of prime factors of 441 is (3 + 3 + 7 + 7) / 4 = 5.00.

• 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

Can you help Rubel in arranging 441 blocks in order to form a rectangle in all possible ways? For arranging 441 blocks in order to form a rectangle in all possible ways we need to find factors of 441 in pair.

Factors of 441 are 1, 3, 7, 9, 21, 49, 63, 147, 441. So, factors of 441 in pair are (1,441), (3,147), (7,63), (9,49), (21,21).

How many total number of factors of 441 in pair are possible?

Factors of 441 are 1, 3, 7, 9, 21, 49, 63, 147, 441. Hence, the factors of 441 in pair are (1,441), (3,147), (7,63), (9,49), (21,21). Therefore, in total 5 pairs of factors are possible.

Sammy wants to write all the negative factors of 441 in pair, but don't know how to start. Help Sammy in writing all the factor pairs.

Negative factors of 441 are -1, -3, -7, -9, -21, -49, -63, -147, -441. Hence, factors of 441 in pair are (-1,-441), (-3,-147), (-7,-63), (-9,-49), (-21,-21).

Find the product of all prime factors of 441.

Factors of 441 are 1, 3, 7, 9, 21, 49, 63, 147, 441. Prime factors are 3, 3, 7, 7. So, the product of all prime factors of 441 would be 3 x 3 x 7 x 7 = 441.

A student has been assigned the following tasks by the teacher:
- Finding out all positive factors of 441.
- Writing all prime factors of 441.
- Writing all the possible factors of 441 in pair.
Help him in writing all these.

Positive factors of 441 are 1, 3, 7, 9, 21, 49, 63, 147, 441.
Prime factors of 441 are 3, 3, 7, 7.
Factors of 441 in pair are (1,441), (3,147), (7,63), (9,49), (21,21).

Can you help Sammy list the factors of 441 and also find the factor pairs?

Factors of 441 are 1, 3, 7, 9, 21, 49, 63, 147, 441.
Factors of 441 in pair are (1,441), (3,147), (7,63), (9,49), (21,21).

Help Diji in finding factors of 441 by Prime Factorization method and then sorting factors of 441 in pairs.

Prime factorization of 441 is 3 x 3 x 7 x 7. Factors of 441 in pair can be written as (1,441), (3,147), (7,63), (9,49), (21,21).

Write the smallest prime factor of 441.

Smallest prime factor of 441 is 3.