# Factors of 1225

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

#### How to find factors of a number

 1.   Find factors of 1225 using Division Method 2.   Find factors of 1225 using Prime Factorization 3.   Find factors of 1225 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 1225

• Divide 1225 by 1: 1225 ÷ 1 : Remainder = 0
• Divide 1225 by 5: 1225 ÷ 5 : Remainder = 0
• Divide 1225 by 7: 1225 ÷ 7 : Remainder = 0
• Divide 1225 by 25: 1225 ÷ 25 : Remainder = 0
• Divide 1225 by 35: 1225 ÷ 35 : Remainder = 0
• Divide 1225 by 49: 1225 ÷ 49 : Remainder = 0
• Divide 1225 by 175: 1225 ÷ 175 : Remainder = 0
• Divide 1225 by 245: 1225 ÷ 245 : Remainder = 0
• Divide 1225 by 1225: 1225 ÷ 1225 : Remainder = 0

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

#### 2. Steps to find factors of 1225 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

#### Method 1: Division Method

To find the primefactors of 1225 using the division method, follow these steps:

• Step 1. Start dividing 1225 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
• Step 2. After finding the smallest prime factor of the number 1225, which is 5. Divide 1225 by 5 to obtain the quotient (245).
1225 ÷ 5 = 245
• Step 3. Repeat step 1 with the obtained quotient (245).
245 ÷ 5 = 49
49 ÷ 7 = 7
7 ÷ 7 = 1

So, the prime factorization of 1225 is, 1225 = 5 x 5 x 7 x 7.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 1225 as shown below:

So, the prime factorization of 1225 is, 1225 = 5 x 5 x 7 x 7.

#### 3. Find factors of 1225 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 1225 would be the two numbers which, when multiplied, give 1225 as the result.

The following table represents the calculation of factors of 1225 in pairs:

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 ) , ( -5 , -245 ) , ( -7 , -175 ) , ( -25 , -49 ) and ( -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.

• What are the prime factors of 1225?

The factors of 1225 are 1, 5, 7, 25, 35, 49, 175, 245, 1225.
Prime factors of 1225 are 5, 5, 7, 7.

• What is the sum of all factors of 1225?

The sum of all factors of 1225 is 1767.

• What are the pair factors of 1225?

Pair factors of 1225 are (1,1225), (5,245), (7,175), (25,49), (35,35).

• What two numbers make 1225?

Two numbers that make 1225 are 5 and 245.

• What are multiples of 1225?

First five multiples of 1225 are 2450, 3675, 4900, 6125.

• Is 1225 a perfect square?

Yes 1225 is a perfect square.

• Which is greatest factor of 1225?

The greatest factor of 1225 is 245.

• How do you factors of 1225?

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

• What are five multiples of 1225?

First five multiples of 1225 are 2450, 3675, 4900, 6125, 7350.

#### Examples of Factors

Can you help Rubel to find out the product of the even factors of 1225?

Factors of 1225 are 1, 5, 7, 25, 35, 49, 175, 245, 1225.
Even factors of 1225 are 0.
Hence, product of even factors of 1225 is; 0 = 0.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 1225? Help her in writing all the factors.

Positive factors are 1, 5, 7, 25, 35, 49, 175, 245, 1225.
Negative factors are -1, -5, -7, -25, -35, -49, -175, -245, -1225.

How many factors are there for 1225?

Factors of 1225 are 1, 5, 7, 25, 35, 49, 175, 245, 1225.
So there are in total 9 factors.

Sammy is puzzled while calculating the prime factors of 1225. Can you help him find them?

Factors of 1225 are 1, 5, 7, 25, 35, 49, 175, 245, 1225.
Prime factors of 1225 are 5, 5, 7, 7

Joey wants to write all the prime factors of 1225 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 1225 are 5, 5, 7, 7.
So in exponential form it can be written as 52 x 72.

What is prime factorization of 1225?

Prime factorization of 1225 is 5 x 5 x 7 x 7 = 52 x 72.

Can you help Rubel to find out the product of the even factors of 1225?

Factors of 1225 are 1, 5, 7, 25, 35, 49, 175, 245, 1225.
Even factors of 1225 are 0.
Hence, product of even factors of 1225 is; 0 = 0.