# Factors of 35 in pair

Factors of 35 in pair are (1, 35) , (5, 7)

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

 1.   Steps to find factors of 35 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 35 in pair

Factor Pair Pair Factorization
1 and 35 1 x 35 = 35
5 and 7 5 x 7 = 35

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 35. They are called negative pair factors.

Hence, the negative pairs of 35 would be ( -1 , -35 ) .

#### 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 35 are 1 , 5 , 7 , 35. So, factors of 35 in pair are (1,35), (5,7).

#### 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 35 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, 5, 7, 35 are exact divisors of 35.
• Factors of 35 are 1, 5, 7, 35. Each factor divides 35 without leaving a remainder.

#### Steps to find Factors of 35

• Step 1. Find all the numbers that would divide 35 without leaving any remainder. Starting with the number 1 upto 17 (half of 35). The number 1 and the number itself are always factors of the given number.
35 ÷ 1 : Remainder = 0
35 ÷ 5 : Remainder = 0
35 ÷ 7 : Remainder = 0
35 ÷ 35 : Remainder = 0

Hence, Factors of 35 are 1, 5, 7, and 35

• Is 35 a perfect square?

No 35 is not a perfect square.

• Write five multiples of 35.

Five multiples of 35 are 70, 105, 140, 175, 210.

• Is there any even prime factor of 35?

No there is no even prime factor, i.e. 2, of 35.

• 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

Can you help Rubel in arranging 35 blocks in order to form a rectangle in all possible ways? For arranging 35 blocks in order to form a rectangle in all possible ways we need to find factors of 35 in pair.

Factors of 35 are 1, 5, 7, 35. So, factors of 35 in pair are (1,35), (5,7).

Ariel has been asked to write all factor pairs of 35 but she is finding it difficult. Can you help her find out?

Factors of 35 are 1, 5, 7, 35. So, factors of 35 in pair are (1,35), (5,7).

How many total number of factors of 35 in pair are possible?

Factors of 35 are 1, 5, 7, 35. Hence, the factors of 35 in pair are (1,35), (5,7). Therefore, in total 2 pairs of factors are possible.

Sammy wants to write all the negative factors of 35 in pair, but don't know how to start. Help Sammy in writing all the factor pairs.

Negative factors of 35 are -1, -5, -7, -35. Hence, factors of 35 in pair are (-1,-35), (-5,-7).

Help Deep in writing the positive factors of 35 in pair and negative factor of 35 in pair.

Factors of 35 are 1, 5, 7, 35. Positive factors of 35 in pair are (1,35), (5,7). Negative factors of 35 in pair are (-1,-35), (-5,-7).

Find the product of all factors of 35.

Factors of 35 are 1, 5, 7, 35. So the product of all factors of 35 would be 1 x 5 x 7 x 35 = 1225.

Find the product of all prime factors of 35.

Factors of 35 are 1, 5, 7, 35. Prime factors are 5, 7. So, the product of all prime factors of 35 would be 5 x 7 = 35.

A student has been assigned the following tasks by the teacher:
- Finding out all positive factors of 35.
- Writing all prime factors of 35.
- Writing all the possible factors of 35 in pair.
Help him in writing all these.

Positive factors of 35 are 1, 5, 7, 35.
Prime factors of 35 are 5, 7.
Factors of 35 in pair are (1,35), (5,7).