Factors of 490

Similarly, as we learned above, factors of 490 are such numbers that will be multiplied to get 490. There are both positive and negative factors of numbers that we will learn as we move ahead in the topic.

490 has only twelve factors: 1, 2, 5, 7, 10, 14, 35, 49, 70, 98, 245, and 490.

Negative factors of 490: Negative factors are nothing but the negative counterparts of the position factors of a number.

Since 490 has twelve positive factors: 1, 2, 5, 7, 10, 14, 35, 49, 70, 98, 245, and, 490, it will also have twelve negative counterparts:  -1, -2, -5, -7, -10, -14, -35, -49, -70, -98, -245, and, - 490.

Prime factors of 490: Since 490 is a composite number, it has 2, 5, and 7 as its prime factor.

Prime factorization of 490:Prime factorization of a number is the method of expressing 490 as a product of prime factors.

The prime factorization of 490 = 2× 5× 7².
 

There are several ways of finding factors of 490. We will learn about them one by one as we go on.
 

In this method, we will try to find such a pair of numbers that will give 490 as their product. We recommend that you should follow the following steps to find factors using multiplication.

Step 1: Always look for a pair of numbers whose product is 490.

Step 2: After finding such pairs, list them all one by one.

Here, factor pairs of 490 are (1, 490), (2, 245), (5, 98), (7, 70), (10, 49), and (14, 35).

So the factors of 490 are 1, 2, 5, 7, 10, 14, 35, 49, 70, 98, 245, and, 490.

In the method, we need to find such numbers that divide 490 completely without leaving any remainder.

490/1 = 490

490/ 2 = 89

490/ 5 = 98

490/ 7 = 70

490/ 10 = 49

490/ 14 = 35

490/ 35 = 14

490/ 49 = 10

490/ 70 = 7

490/ 98 = 5

490/ 245 = 2

490/ 490 = 1

All the 12 numbers: 1, 2, 5, 7, 10, 14, 35, 49, 70, 98, 245, and, 490, mentioned above divide 490 completely without any remainder. Hence, they are factors of 490.
 

In the prime factorization method, a number is expressed as the product of prime factors.

Here, as we know, 490 = 2 × 5 × 7²

 2, 5, and 7 are the prime factors when multiplied together will give 490 as a product of the multiplication.
 

Factor tree is a graphical representation of factors of any number. In the diagram, each branch represents the prime factors a number has.
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The factor pairs of a number refer to a pair of numbers which, when multiplied, will give the number as a product.

 The factor pairs of 490 are (1, 490), (2, 245), (5, 98), (7, 70), (10, 49), and (14, 35)

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

Negative Pair Factors of 490 are (-1, -490), (-2, -245), (-5, -98), (-7, -70), (-10, -49), and (-14, -35)

• Prime Numbers: Those numbers which have no other factors other than 1 & the number itself.

• Composite Numbers: Those numbers that have more than 2 factors.

• Negative Factors: These are the counterparts of the positive factors of a number.

• Prime Factorization: Process of breaking down a composite number into products of several of its prime factors.