# Factors of 306 in pair

Factors of 306 in pair are (1, 306) , (2, 153) , (3, 102) , (6, 51) , (9, 34) and (17, 18)

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

 1.   Steps to find factors of 306 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 306 in pair

Factor Pair Pair Factorization
1 and 306 1 x 306 = 306
2 and 153 2 x 153 = 306
3 and 102 3 x 102 = 306
6 and 51 6 x 51 = 306
9 and 34 9 x 34 = 306
17 and 18 17 x 18 = 306

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 306. They are called negative pair factors.

Hence, the negative pairs of 306 would be ( -1 , -306 ) .

#### 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 306 are 1 , 2 , 3 , 6 , 9 , 17 , 18 , 34 , 51 , 102 , 153 , 306. So, factors of 306 in pair are (1,306), (2,153), (3,102), (6,51), (9,34), (17,18).

#### 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

• Each number is a factor of itself. Eg. 306 is a factor of itself.
• 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, 6, 9, 17, 18, 34, 51, 102, 153, 306 are exact divisors of 306.
• 1 is a factor of every number. Eg. 1 is a factor of 306.
• Every number is a factor of zero (0), since 306 x 0 = 0.

#### Steps to find Factors of 306

• Step 1. Find all the numbers that would divide 306 without leaving any remainder. Starting with the number 1 upto 153 (half of 306). The number 1 and the number itself are always factors of the given number.
306 ÷ 1 : Remainder = 0
306 ÷ 2 : Remainder = 0
306 ÷ 3 : Remainder = 0
306 ÷ 6 : Remainder = 0
306 ÷ 9 : Remainder = 0
306 ÷ 17 : Remainder = 0
306 ÷ 18 : Remainder = 0
306 ÷ 34 : Remainder = 0
306 ÷ 51 : Remainder = 0
306 ÷ 102 : Remainder = 0
306 ÷ 153 : Remainder = 0
306 ÷ 306 : Remainder = 0

Hence, Factors of 306 are 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, and 306

• Is 306 a composite number?

Yes 306 is a composite number.

• Is 306 a prime number?

No 306 is not a prime number.

• What is the mean of factors of 306?

Factors of 306 are 1 , 2 , 3 , 6 , 9 , 17 , 18 , 34 , 51 , 102 , 153 , 306. therefore mean of factors of 306 is (1 + 2 + 3 + 6 + 9 + 17 + 18 + 34 + 51 + 102 + 153 + 306) / 12 = 58.50.

• 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

Ariel has been asked to write all factor pairs of 306 but she is finding it difficult. Can you help her find out?

Factors of 306 are 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 306. So, factors of 306 in pair are (1,306), (2,153), (3,102), (6,51), (9,34), (17,18).

Sammy wants to write all the negative factors of 306 in pair, but don't know how to start. Help Sammy in writing all the factor pairs.

Negative factors of 306 are -1, -2, -3, -6, -9, -17, -18, -34, -51, -102, -153, -306. Hence, factors of 306 in pair are (-1,-306), (-2,-153), (-3,-102), (-6,-51), (-9,-34), (-17,-18).

Help Deep in writing the positive factors of 306 in pair and negative factor of 306 in pair.

Factors of 306 are 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 306. Positive factors of 306 in pair are (1,306), (2,153), (3,102), (6,51), (9,34), (17,18). Negative factors of 306 in pair are (-1,-306), (-2,-153), (-3,-102), (-6,-51), (-9,-34), (-17,-18).

Find the product of all prime factors of 306.

Factors of 306 are 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 306. Prime factors are 2, 3, 3, 17. So, the product of all prime factors of 306 would be 2 x 3 x 3 x 17 = 306.

Can you help Sammy list the factors of 306 and also find the factor pairs?

Factors of 306 are 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 306.
Factors of 306 in pair are (1,306), (2,153), (3,102), (6,51), (9,34), (17,18).

Help Diji in finding factors of 306 by Prime Factorization method and then sorting factors of 306 in pairs.

Prime factorization of 306 is 2 x 3 x 3 x 17. Factors of 306 in pair can be written as (1,306), (2,153), (3,102), (6,51), (9,34), (17,18).

Write the smallest prime factor of 306.

Smallest prime factor of 306 is 2.

Write the largest prime factor of 306.

Largest prime factor of 306 is 17.