# Factors of 1521 in pair

Factors of 1521 in pair are (1, 1521) , (3, 507) , (9, 169) , (13, 117) and (39, 39)

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

 1.   Steps to find factors of 1521 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 1521 in pair

Factor Pair Pair Factorization
1 and 1521 1 x 1521 = 1521
3 and 507 3 x 507 = 1521
9 and 169 9 x 169 = 1521
13 and 117 13 x 117 = 1521
39 and 39 39 x 39 = 1521

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 1521. They are called negative pair factors.

Hence, the negative pairs of 1521 would be ( -1 , -1521 ) .

#### 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 1521 are 1 , 3 , 9 , 13 , 39 , 117 , 169 , 507 , 1521. So, factors of 1521 in pair are (1,1521), (3,507), (9,169), (13,117), (39,39).

#### 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, 9, 13, 39, 117, 169, 507, 1521 are exact divisors of 1521.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Each number is a factor of itself. Eg. 1521 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 1521.

#### Steps to find Factors of 1521

• Step 1. Find all the numbers that would divide 1521 without leaving any remainder. Starting with the number 1 upto 760 (half of 1521). The number 1 and the number itself are always factors of the given number.
1521 ÷ 1 : Remainder = 0
1521 ÷ 3 : Remainder = 0
1521 ÷ 9 : Remainder = 0
1521 ÷ 13 : Remainder = 0
1521 ÷ 39 : Remainder = 0
1521 ÷ 117 : Remainder = 0
1521 ÷ 169 : Remainder = 0
1521 ÷ 507 : Remainder = 0
1521 ÷ 1521 : Remainder = 0

Hence, Factors of 1521 are 1, 3, 9, 13, 39, 117, 169, 507, and 1521

• Is 1521 a composite number?

Yes 1521 is a composite number.

• Is 1521 a perfect square?

Yes 1521 is a perfect square.

• Write all odd factors of 1521?

The factors of 1521 are 1, 3, 9, 13, 39, 117, 169, 507, 1521.
Odd factors of 1521 are 1 , 3 , 9 , 13 , 39 , 117 , 169 , 507 , 1521.

• What is the mean of all prime factors of 1521?

Factors of 1521 are 1 , 3 , 9 , 13 , 39 , 117 , 169 , 507 , 1521. Prime factors of 1521 are 3 , 3 , 13 , 13. Therefore mean of prime factors of 1521 is (3 + 3 + 13 + 13) / 4 = 8.00.

• 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 1521 blocks in order to form a rectangle in all possible ways? For arranging 1521 blocks in order to form a rectangle in all possible ways we need to find factors of 1521 in pair.

Factors of 1521 are 1, 3, 9, 13, 39, 117, 169, 507, 1521. So, factors of 1521 in pair are (1,1521), (3,507), (9,169), (13,117), (39,39).

How many total number of factors of 1521 in pair are possible?

Factors of 1521 are 1, 3, 9, 13, 39, 117, 169, 507, 1521. Hence, the factors of 1521 in pair are (1,1521), (3,507), (9,169), (13,117), (39,39). Therefore, in total 5 pairs of factors are possible.

Sammy wants to write all the negative factors of 1521 in pair, but don't know how to start. Help Sammy in writing all the factor pairs.

Negative factors of 1521 are -1, -3, -9, -13, -39, -117, -169, -507, -1521. Hence, factors of 1521 in pair are (-1,-1521), (-3,-507), (-9,-169), (-13,-117), (-39,-39).

Find the product of all prime factors of 1521.

Factors of 1521 are 1, 3, 9, 13, 39, 117, 169, 507, 1521. Prime factors are 3, 3, 13, 13. So, the product of all prime factors of 1521 would be 3 x 3 x 13 x 13 = 1521.

A student has been assigned the following tasks by the teacher:
- Finding out all positive factors of 1521.
- Writing all prime factors of 1521.
- Writing all the possible factors of 1521 in pair.
Help him in writing all these.

Positive factors of 1521 are 1, 3, 9, 13, 39, 117, 169, 507, 1521.
Prime factors of 1521 are 3, 3, 13, 13.
Factors of 1521 in pair are (1,1521), (3,507), (9,169), (13,117), (39,39).

Can you help Sammy list the factors of 1521 and also find the factor pairs?

Factors of 1521 are 1, 3, 9, 13, 39, 117, 169, 507, 1521.
Factors of 1521 in pair are (1,1521), (3,507), (9,169), (13,117), (39,39).

Help Diji in finding factors of 1521 by Prime Factorization method and then sorting factors of 1521 in pairs.

Prime factorization of 1521 is 3 x 3 x 13 x 13. Factors of 1521 in pair can be written as (1,1521), (3,507), (9,169), (13,117), (39,39).

Write the smallest prime factor of 1521.

Smallest prime factor of 1521 is 3.