# Factors of 75 in pair

Factors of 75 in pair are (1, 75) , (3, 25) and (5, 15)

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

 1.   Steps to find factors of 75 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 75 in pair

Factor Pair Pair Factorization
1 and 75 1 x 75 = 75
3 and 25 3 x 25 = 75
5 and 15 5 x 15 = 75

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 75. They are called negative pair factors.

Hence, the negative pairs of 75 would be ( -1 , -75 ) .

#### Definition of factor pairs?

In mathematics, factor pair are often given as pair of numbers which when multiplied together give the original number. Every natural number is a product of atleast one factor pair. Eg- Factors of 75 are 1 , 3 , 5 , 15 , 25 , 75. So, factors of 75 in pair are (1,75), (3,25), (5,15).

#### What are factors?

In mathematics, a factor is that number which divides into another number exactly, without leaving a remainder. A factor of a number can be positive or negative.

#### Properties of Factors

• Every number is a factor of zero (0), since 75 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, 5, 15, 25, 75 are exact divisors of 75.
• Factors of 75 are 1, 3, 5, 15, 25, 75. Each factor divides 75 without leaving a remainder.

#### Steps to find Factors of 75

• Step 1. Find all the numbers that would divide 75 without leaving any remainder. Starting with the number 1 upto 37 (half of 75). The number 1 and the number itself are always factors of the given number.
75 ÷ 1 : Remainder = 0
75 ÷ 3 : Remainder = 0
75 ÷ 5 : Remainder = 0
75 ÷ 15 : Remainder = 0
75 ÷ 25 : Remainder = 0
75 ÷ 75 : Remainder = 0

Hence, Factors of 75 are 1, 3, 5, 15, 25, and 75

• Is 75 a composite number?

Yes 75 is a composite number.

• Is 75 a perfect square?

No 75 is not a perfect square.

• Write all odd factors of 75?

The factors of 75 are 1, 3, 5, 15, 25, 75.
Odd factors of 75 are 1 , 3 , 5 , 15 , 25 , 75.

• What is the mean of all prime factors of 75?

Factors of 75 are 1 , 3 , 5 , 15 , 25 , 75. Prime factors of 75 are 3 , 5 , 5. Therefore mean of prime factors of 75 is (3 + 5 + 5) / 3 = 4.33.

• 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.

#### Examples of Factors

Can you help Rubel in arranging 75 blocks in order to form a rectangle in all possible ways? For arranging 75 blocks in order to form a rectangle in all possible ways we need to find factors of 75 in pair.

Factors of 75 are 1, 3, 5, 15, 25, 75. So, factors of 75 in pair are (1,75), (3,25), (5,15).

Ariel has been asked to write all factor pairs of 75 but she is finding it difficult. Can you help her find out?

Factors of 75 are 1, 3, 5, 15, 25, 75. So, factors of 75 in pair are (1,75), (3,25), (5,15).

How many total number of factors of 75 in pair are possible?

Factors of 75 are 1, 3, 5, 15, 25, 75. Hence, the factors of 75 in pair are (1,75), (3,25), (5,15). Therefore, in total 3 pairs of factors are possible.

Sammy wants to write all the negative factors of 75 in pair, but don't know how to start. Help Sammy in writing all the factor pairs.

Negative factors of 75 are -1, -3, -5, -15, -25, -75. Hence, factors of 75 in pair are (-1,-75), (-3,-25), (-5,-15).

Help Deep in writing the positive factors of 75 in pair and negative factor of 75 in pair.

Factors of 75 are 1, 3, 5, 15, 25, 75. Positive factors of 75 in pair are (1,75), (3,25), (5,15). Negative factors of 75 in pair are (-1,-75), (-3,-25), (-5,-15).

Find the product of all factors of 75.

Factors of 75 are 1, 3, 5, 15, 25, 75. So the product of all factors of 75 would be 1 x 3 x 5 x 15 x 25 x 75 = 421875.

Find the product of all prime factors of 75.

Factors of 75 are 1, 3, 5, 15, 25, 75. Prime factors are 3, 5, 5. So, the product of all prime factors of 75 would be 3 x 5 x 5 = 75.

A student has been assigned the following tasks by the teacher:
- Finding out all positive factors of 75.
- Writing all prime factors of 75.
- Writing all the possible factors of 75 in pair.
Help him in writing all these.

Positive factors of 75 are 1, 3, 5, 15, 25, 75.
Prime factors of 75 are 3, 5, 5.
Factors of 75 in pair are (1,75), (3,25), (5,15).