# Factors of 245

Factors of 245 are 1, 5, 7, 35, 49, and 245

#### How to find factors of a number

 1.   Find factors of 245 using Division Method 2.   Find factors of 245 using Prime Factorization 3.   Find factors of 245 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 245

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

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

#### 2. Steps to find factors of 245 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 245 using the division method, follow these steps:

• Step 1. Start dividing 245 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 245, which is 5. Divide 245 by 5 to obtain the quotient (49).
245 ÷ 5 = 49
• Step 3. Repeat step 1 with the obtained quotient (49).
49 ÷ 7 = 7
7 ÷ 7 = 1

So, the prime factorization of 245 is, 245 = 5 x 7 x 7.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 245 as shown below:

So, the prime factorization of 245 is, 245 = 5 x 7 x 7.

#### 3. Find factors of 245 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 245 would be the two numbers which, when multiplied, give 245 as the result.

The following table represents the calculation of factors of 245 in pairs:

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

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 245. They are called negative pair factors.

Hence, the negative pairs of 245 would be ( -1 , -245 ) , ( -5 , -49 ) and ( -7 , -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, 35, 49, 245 are exact divisors of 245.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Each number is a factor of itself. Eg. 245 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 245.

• What two numbers make 245?

Two numbers that make 245 are 5 and 49.

• What is prime factorization of 245?

Prime factorization of 245 is 5 x 7 x 7.

• Write some multiples of 245?

First five multiples of 245 are 490, 735, 980, 1225.

• Which is the smallest prime factor of 245?

The smallest prime factor of 245 is 5.

• Is 245 a perfect square?

No 245 is not a perfect square.

• What is the sum of all factors of 245?

The sum of all factors of 245 is 342.

• What are factors of 245?

Factors of 245 are 1, 5, 7, 35, 49, 245.

• How do you find factors of a negative number? ( eg. -245 )?

Factors of -245 are -1, -5, -7, -35, -49, -245.

• Is 245 a whole number?

Yes 245 is a whole number.

#### Examples of Factors

Joy wants to calculate mean of all the factors of 245. Help him in finding the mean of 245.

Factors of 245 are 1, 5, 7, 35, 49, 245.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 245 is 1 + 5 + 7 + 35 + 49 + 245 = 342.
Hence, the mean of factors of 245 is 342 ÷ 6 = 57.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 245? Help her in writing all the factors.

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

Joey wants to write all the prime factors of 245 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 245 are 5, 7, 7.
So in exponential form it can be written as 5 x 72.

Kevin has been asked to write 5 factor(s) of 245. Can you predict the answer?

5 factor(s) of 245 are 1, 5, 7, 35, 49.

Sammy is puzzled while calculating the prime factors of 245. Can you help him find them?

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

What is prime factorization of 245?

Prime factorization of 245 is 5 x 7 x 7 = 5 x 72.

Can you help Rubel to find out the product of the even factors of 245?

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