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Factors of 490

Factors of 490 are the list of integers that can be evenly divided into 490. There are overall 12 factors of 490 among which 490 is the biggest factor and its prime factors are 2, 5, 7. The Prime Factorization of 490 is 2¹ × 5¹ × 7².

All Factors of 490: 1, 2, 5, 7, 10, 14, 35, 49, 70, 98, 245 and 490
Prime Factors of 490: 2, 5, 7
Prime Factorization of 490: 2¹ × 5¹ × 7²
Sum of Factors of 490: 1026

1.	What Are the Factors of 490?
2.	Factors of 490 by Prime Factorization
3.	Factors of 490 in Pairs
4.	FAQs on Factors of 490

What are Factors of 490?

Factors of 490 are pairs of those numbers whose products result in 490. These factors are either prime numbers or composite numbers.

How to Find the Factors of 490?

To find the factors of 490, we will have to find the list of numbers that would divide 490 without leaving any remainder.

490/14 = 35; therefore, 14 is a factor of 490 and 35 is also a factor of 490.
490/70 = 7; therefore, 70 is a factor of 490 and 7 is also a factor of 490.

Similarly we can find other factors. Hence, the factors of 490 are 1, 2, 5, 7, 10, 14, 35, 49, 70, 98, 245, 490.

☛ Also Check:

Factors of 41 - The factors of 41 are 1, 41
Factors of 144 - The factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
Factors of 12 - The factors of 12 are 1, 2, 3, 4, 6, 12
Factors of 66 - The factors of 66 are 1, 2, 3, 6, 11, 22, 33, 66
Factors of 56 - The factors of 56 are 1, 2, 4, 7, 8, 14, 28, 56

Factors of 490 by Prime Factorization

The number 490 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 490. The first step is to divide the number 490 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.

490 ÷ 2 = 245

Further dividing 245 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 245 by the next smallest prime factor. We stop ultimately if the next prime factor doesn't exist or when we can't divide any further.

So, the prime factorization of 490 can be written as 2¹ × 5¹ × 7² where 2, 5, 7 are prime.

Factors of 490 in Pairs

Pair factors of 490 are the pairs of numbers that when multiplied give the product 490. The factors of 490 in pairs are:

1 × 490 = (1, 490)
2 × 245 = (2, 245)
5 × 98 = (5, 98)
7 × 70 = (7, 70)
10 × 49 = (10, 49)
14 × 35 = (14, 35)

Negative pair factors of 490 are:

-1 × -490 = (-1, -490)
-2 × -245 = (-2, -245)
-5 × -98 = (-5, -98)
-7 × -70 = (-7, -70)
-10 × -49 = (-10, -49)
-14 × -35 = (-14, -35)

NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.

Factors of 490 Solved Examples

Example 1: How many factors are there for 490?

Solution:

The factors of 490 are too many, therefore if we can find the prime factorization of 490, then the total number of factors can be calculated using the formula shown below.
If the prime factorization of the number is a^x × b^y × c^z where a, b, c are prime, then the total number of factors can be given by (x + 1)(y + 1)(z + 1).

Prime Factorization of 490 = 2¹ × 5¹ × 7²
Therefore, the total number of factors are (1 + 1) × (1 + 1) × (2 + 1) = 2 × 2 × 3 = 12
Example 2: Find the LCM and Greatest Common Factor (GCF) of 490 and 337.

Solution:

The factors of 490 are 1, 2, 5, 7, 10, 14, 35, 49, 70, 98, 245, 490 and factors of 337 are 1, 337.

Therefore, the LCM of 490 and 337 is 165130 and Greatest Common Factor (GCF) of 490 and 337 is 1.
Example 3: Find if 1, 7, 10, 14, 49, 456 and 490 are factors of 490.

Solution:

When we divide 490 by 456 it leaves a remainder. Therefore, the number 456 is not a factor of 490. All numbers except 456 are factors of 490.
Example 4: Find the product of all the prime factors of 490.

Solution:

Since, the prime factors of 490 are 2, 5, 7. Therefore, the product of prime factors = 2 × 5 × 7 = 70.

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FAQs on Factors of 490

What are the Factors of 490?

The factors of 490 are 1, 2, 5, 7, 10, 14, 35, 49, 70, 98, 245, 490 and its negative factors are -1, -2, -5, -7, -10, -14, -35, -49, -70, -98, -245, -490.

What is the Sum of Factors of 490?

Sum of all factors of 490 = (2^{1 + 1} - 1)/(2 - 1) × (5^{1 + 1} - 1)/(5 - 1) × (7^{2 + 1} - 1)/(7 - 1) = 1026

What numbers are the Pair Factors of 490?

The pair factors of 490 are (1, 490), (2, 245), (5, 98), (7, 70), (10, 49), (14, 35).

What is the Greatest Common Factor of 490 and 425?

The factors of 490 and 425 are 1, 2, 5, 7, 10, 14, 35, 49, 70, 98, 245, 490 and 1, 5, 17, 25, 85, 425 respectively.

Common factors of 490 and 425 are [1, 5].

Hence, the Greatest Common Factor of 490 and 425 is 5.

What are the Common Factors of 490 and 255?

Since, the factors of 490 are 1, 2, 5, 7, 10, 14, 35, 49, 70, 98, 245, 490 and the factors of 255 are 1, 3, 5, 15, 17, 51, 85, 255.
Hence, [1, 5] are the common factors of 490 and 255.

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