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Factors of 676

Factors of 676 are numbers that, when multiplied in pairs give the product as 676. There are total 9 factors of 676 i.e. 1, 2, 4, 13, 26, 52, 169, 338, 676. The Prime Factors of 676 are 2 × 13 and its Factors in Pairs are (1, 676), (2, 338), (4, 169), (13, 52), (26, 26).

All Factors of 676: 1, 2, 4, 13, 26, 52, 169, 338 and 676
Negative Factors of 676: -1, -2, -4, -13, -26, -52, -169, -338 and -676
Prime Factors of 676: 2, 13
Prime Factorization of 676: 2² × 13²
Sum of Factors of 676: 1281

1.	What Are the Factors of 676?
2.	Factors of 676 by Prime Factorization
3.	Factors of 676 in Pairs
4.	FAQs on Factors of 676

What are Factors of 676?

Factors of 676 are pairs of those numbers whose products result in 676. These factors are either prime numbers or composite numbers.

How to Find the Factors of 676?

To find the factors of 676, we will have to find the list of numbers that would divide 676 without leaving any remainder.

676/52 = 13; therefore, 52 is a factor of 676 and 13 is also a factor of 676.
676/169 = 4; therefore, 169 is a factor of 676 and 4 is also a factor of 676.

Similarly we can find other factors. Hence, the factors of 676 are 1, 2, 4, 13, 26, 52, 169, 338, 676.

☛ Also Check:

Factors of 40 - The factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40
Factors of 15 - The factors of 15 are 1, 3, 5, 15
Factors of 7 - The factors of 7 are 1, 7
Factors of 14 - The factors of 14 are 1, 2, 7, 14
Factors of 30 - The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30

Factors of 676 by Prime Factorization

The number 676 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 676. The first step is to divide the number 676 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.

676 ÷ 2 = 338
338 ÷ 2 = 169

Further dividing 169 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 169 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 676 can be written as 2² × 13² where 2, 13 are prime.

Factors of 676 in Pairs

Pair factors of 676 are the pairs of numbers that when multiplied give the product 676. The factors of 676 in pairs are:

1 × 676 = (1, 676)
2 × 338 = (2, 338)
4 × 169 = (4, 169)
13 × 52 = (13, 52)
26 × 26 = (26, 26)

Negative pair factors of 676 are:

-1 × -676 = (-1, -676)
-2 × -338 = (-2, -338)
-4 × -169 = (-4, -169)
-13 × -52 = (-13, -52)
-26 × -26 = (-26, -26)

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

Factors of 676 Solved Examples

Example 1: How many factors are there for 676?

Solution:

The factors of 676 are too many, therefore if we can find the prime factorization of 676, 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 676 = 2² × 13²
Therefore, the total number of factors are (2 + 1) × (2 + 1) = 3 × 3 = 9
Example 2: Find the Least Common Multiple (LCM) and Greatest Common Divisor (GCD) of 676 and 417.

Solution:

The factors of 676 are 1, 2, 4, 13, 26, 52, 169, 338, 676 and factors of 417 are 1, 3, 139, 417.

Therefore, the Least Common Multiple (LCM) of 676 and 417 is 281892 and Greatest Common Divisor (GCD) of 676 and 417 is 1.
Example 3: Find if 1, 13, 52, 191 and 676 are factors of 676.

Solution:

When we divide 676 by 191 it leaves a remainder. Therefore, the number 191 is not a factor of 676. All numbers except 191 are factors of 676.
Example 4: Find the product of all the prime factors of 676.

Solution:

Since, the prime factors of 676 are 2, 13. Therefore, the product of prime factors = 2 × 13 = 26.

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FAQs on Factors of 676

What are the Factors of 676?

The factors of 676 are 1, 2, 4, 13, 26, 52, 169, 338, 676 and its negative factors are -1, -2, -4, -13, -26, -52, -169, -338, -676.

What is the Sum of Factors of 676?

Sum of all factors of 676 = (2^{2 + 1} - 1)/(2 - 1) × (13^{2 + 1} - 1)/(13 - 1) = 1281

What are Prime Factors of 676?

The prime factors of 676 are 2, 13.

What is the Greatest Common Factor of 676 and 276?

The factors of 676 and 276 are 1, 2, 4, 13, 26, 52, 169, 338, 676 and 1, 2, 3, 4, 6, 12, 23, 46, 69, 92, 138, 276 respectively.

Common factors of 676 and 276 are [1, 2, 4].

Hence, the Greatest Common Factor of 676 and 276 is 4.

How Many Factors of 676 are also common to the Factors of 177?

Since, the factors of 676 are 1, 2, 4, 13, 26, 52, 169, 338, 676 and factors of 177 are 1, 3, 59, 177. Hence, 676 and 177 have only one common factor which is 1. Therefore, 676 and 177 are co-prime.

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