# Factors of 1225 in pair

Factors of 1225 in pair are (1, 1225) , (5, 245) , (7, 175) , (25, 49) and (35, 35)

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

 1.   Steps to find factors of 1225 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 1225 in pair

Factor Pair Pair Factorization
1 and 1225 1 x 1225 = 1225
5 and 245 5 x 245 = 1225
7 and 175 7 x 175 = 1225
25 and 49 25 x 49 = 1225
35 and 35 35 x 35 = 1225

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 1225. They are called negative pair factors.

Hence, the negative pairs of 1225 would be ( -1 , -1225 ) .

#### 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 1225 are 1 , 5 , 7 , 25 , 35 , 49 , 175 , 245 , 1225. So, factors of 1225 in pair are (1,1225), (5,245), (7,175), (25,49), (35,35).

#### 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 factor of a number is an exact divisor of that number, example 1, 5, 7, 25, 35, 49, 175, 245, 1225 are exact divisors of 1225.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Each number is a factor of itself. Eg. 1225 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 1225.

#### Steps to find Factors of 1225

• Step 1. Find all the numbers that would divide 1225 without leaving any remainder. Starting with the number 1 upto 612 (half of 1225). The number 1 and the number itself are always factors of the given number.
1225 ÷ 1 : Remainder = 0
1225 ÷ 5 : Remainder = 0
1225 ÷ 7 : Remainder = 0
1225 ÷ 25 : Remainder = 0
1225 ÷ 35 : Remainder = 0
1225 ÷ 49 : Remainder = 0
1225 ÷ 175 : Remainder = 0
1225 ÷ 245 : Remainder = 0
1225 ÷ 1225 : Remainder = 0

Hence, Factors of 1225 are 1, 5, 7, 25, 35, 49, 175, 245, and 1225

• Is there any even prime factor of 1225?

No there is no even prime factor, i.e. 2, of 1225.

• What is the mean of all prime factors of 1225?

Factors of 1225 are 1 , 5 , 7 , 25 , 35 , 49 , 175 , 245 , 1225. Prime factors of 1225 are 5 , 5 , 7 , 7. Therefore mean of prime factors of 1225 is (5 + 5 + 7 + 7) / 4 = 6.00.

• What is the mean of factors of 1225?

Factors of 1225 are 1 , 5 , 7 , 25 , 35 , 49 , 175 , 245 , 1225. therefore mean of factors of 1225 is (1 + 5 + 7 + 25 + 35 + 49 + 175 + 245 + 1225) / 9 = 196.33.

• 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.

• 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 1225 blocks in order to form a rectangle in all possible ways? For arranging 1225 blocks in order to form a rectangle in all possible ways we need to find factors of 1225 in pair.

Factors of 1225 are 1, 5, 7, 25, 35, 49, 175, 245, 1225. So, factors of 1225 in pair are (1,1225), (5,245), (7,175), (25,49), (35,35).

How many total number of factors of 1225 in pair are possible?

Factors of 1225 are 1, 5, 7, 25, 35, 49, 175, 245, 1225. Hence, the factors of 1225 in pair are (1,1225), (5,245), (7,175), (25,49), (35,35). Therefore, in total 5 pairs of factors are possible.

Sammy wants to write all the negative factors of 1225 in pair, but don't know how to start. Help Sammy in writing all the factor pairs.

Negative factors of 1225 are -1, -5, -7, -25, -35, -49, -175, -245, -1225. Hence, factors of 1225 in pair are (-1,-1225), (-5,-245), (-7,-175), (-25,-49), (-35,-35).

Find the product of all prime factors of 1225.

Factors of 1225 are 1, 5, 7, 25, 35, 49, 175, 245, 1225. Prime factors are 5, 5, 7, 7. So, the product of all prime factors of 1225 would be 5 x 5 x 7 x 7 = 1225.

A student has been assigned the following tasks by the teacher:
- Finding out all positive factors of 1225.
- Writing all prime factors of 1225.
- Writing all the possible factors of 1225 in pair.
Help him in writing all these.

Positive factors of 1225 are 1, 5, 7, 25, 35, 49, 175, 245, 1225.
Prime factors of 1225 are 5, 5, 7, 7.
Factors of 1225 in pair are (1,1225), (5,245), (7,175), (25,49), (35,35).

Can you help Sammy list the factors of 1225 and also find the factor pairs?

Factors of 1225 are 1, 5, 7, 25, 35, 49, 175, 245, 1225.
Factors of 1225 in pair are (1,1225), (5,245), (7,175), (25,49), (35,35).

Help Diji in finding factors of 1225 by Prime Factorization method and then sorting factors of 1225 in pairs.

Prime factorization of 1225 is 5 x 5 x 7 x 7. Factors of 1225 in pair can be written as (1,1225), (5,245), (7,175), (25,49), (35,35).

Write the smallest prime factor of 1225.

Smallest prime factor of 1225 is 5.