# Factors of 490

Factors of 490 are 1, 2, 5, 7, 10, 14, 35, 49, 70, 98, 245, and 490

#### How to find factors of a number

 1.   Find factors of 490 using Division Method 2.   Find factors of 490 using Prime Factorization 3.   Find factors of 490 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 490

• Divide 490 by 1: 490 ÷ 1 : Remainder = 0
• Divide 490 by 2: 490 ÷ 2 : Remainder = 0
• Divide 490 by 5: 490 ÷ 5 : Remainder = 0
• Divide 490 by 7: 490 ÷ 7 : Remainder = 0
• Divide 490 by 10: 490 ÷ 10 : Remainder = 0
• Divide 490 by 14: 490 ÷ 14 : Remainder = 0
• Divide 490 by 35: 490 ÷ 35 : Remainder = 0
• Divide 490 by 49: 490 ÷ 49 : Remainder = 0
• Divide 490 by 70: 490 ÷ 70 : Remainder = 0
• Divide 490 by 98: 490 ÷ 98 : Remainder = 0
• Divide 490 by 245: 490 ÷ 245 : Remainder = 0
• Divide 490 by 490: 490 ÷ 490 : Remainder = 0

Hence, Factors of 490 are 1, 2, 5, 7, 10, 14, 35, 49, 70, 98, 245, and 490

#### 2. Steps to find factors of 490 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 490 using the division method, follow these steps:

• Step 1. Start dividing 490 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 490, which is 2. Divide 490 by 2 to obtain the quotient (245).
490 ÷ 2 = 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 490 is, 490 = 2 x 5 x 7 x 7.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 490 as shown below:

So, the prime factorization of 490 is, 490 = 2 x 5 x 7 x 7.

#### 3. Find factors of 490 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 490 would be the two numbers which, when multiplied, give 490 as the result.

The following table represents the calculation of factors of 490 in pairs:

Factor Pair Pair Factorization
1 and 490 1 x 490 = 490
2 and 245 2 x 245 = 490
5 and 98 5 x 98 = 490
7 and 70 7 x 70 = 490
10 and 49 10 x 49 = 490
14 and 35 14 x 35 = 490

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 490. They are called negative pair factors.

Hence, the negative pairs of 490 would be ( -1 , -490 ) , ( -2 , -245 ) , ( -5 , -98 ) , ( -7 , -70 ) , ( -10 , -49 ) and ( -14 , -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

• Each number is a factor of itself. Eg. 490 is a factor of itself.
• 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, 2, 5, 7, 10, 14, 35, 49, 70, 98, 245, 490 are exact divisors of 490.
• 1 is a factor of every number. Eg. 1 is a factor of 490.
• Every number is a factor of zero (0), since 490 x 0 = 0.

• Is 490 a perfect square?

No 490 is not a perfect square.

• What are factors of 490?

Factors of 490 are 1, 2, 5, 7, 10, 14, 35, 49, 70, 98, 245, 490.

• Which is greatest factor of 490?

The greatest factor of 490 is 245.

• What is the sum of all factors of 490?

The sum of all factors of 490 is 1026.

• What are multiples of 490?

First five multiples of 490 are 980, 1470, 1960, 2450.

• What is the greatest prime factors of 490?

The greatest prime factor of 490 is 7.

• What are six multiples of 490?

First five multiples of 490 are 980, 1470, 1960, 2450, 2940, 3430.

• What is prime factorization of 490?

Prime factorization of 490 is 2 x 5 x 7 x 7.

• Is 490 a whole number?

Yes 490 is a whole number.

#### Examples of Factors

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 490? Help her in writing all the factors.

Positive factors are 1, 2, 5, 7, 10, 14, 35, 49, 70, 98, 245, 490.
Negative factors are -1, -2, -5, -7, -10, -14, -35, -49, -70, -98, -245, -490.

Can you help Sammy find out the product of the odd factors of 490?

Factors of 490 are 1, 2, 5, 7, 10, 14, 35, 49, 70, 98, 245, 490.
Odd factors of 490 are 1, 5, 7, 35, 49, 245.
Hence product of odd factors of 490 is; 1 x 5 x 7 x 35 x 49 x 245 = 14706125.

Joey wants to write all the prime factors of 490 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 490 are 2, 5, 7, 7.
So in exponential form it can be written as 2 x 5 x 72.

How many factors are there for 490?

Factors of 490 are 1, 2, 5, 7, 10, 14, 35, 49, 70, 98, 245, 490.
So there are in total 12 factors.

Kevin has been asked to write 11 factor(s) of 490. Can you predict the answer?

11 factor(s) of 490 are 1, 2, 5, 7, 10, 14, 35, 49, 70, 98, 245.

Sammy is puzzled while calculating the prime factors of 490. Can you help him find them?

Factors of 490 are 1, 2, 5, 7, 10, 14, 35, 49, 70, 98, 245, 490.
Prime factors of 490 are 2, 5, 7, 7

What is prime factorization of 490?

Prime factorization of 490 is 2 x 5 x 7 x 7 = 2 x 5 x 72.