# Factors of 676

Factors of 676 are 1, 2, 4, 13, 26, 52, 169, 338, and 676

#### How to find factors of a number

 1.   Find factors of 676 using Division Method 2.   Find factors of 676 using Prime Factorization 3.   Find factors of 676 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 676

• Divide 676 by 1: 676 ÷ 1 : Remainder = 0
• Divide 676 by 2: 676 ÷ 2 : Remainder = 0
• Divide 676 by 4: 676 ÷ 4 : Remainder = 0
• Divide 676 by 13: 676 ÷ 13 : Remainder = 0
• Divide 676 by 26: 676 ÷ 26 : Remainder = 0
• Divide 676 by 52: 676 ÷ 52 : Remainder = 0
• Divide 676 by 169: 676 ÷ 169 : Remainder = 0
• Divide 676 by 338: 676 ÷ 338 : Remainder = 0
• Divide 676 by 676: 676 ÷ 676 : Remainder = 0

Hence, Factors of 676 are 1, 2, 4, 13, 26, 52, 169, 338, and 676

#### 2. Steps to find factors of 676 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 676 using the division method, follow these steps:

• Step 1. Start dividing 676 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 676, which is 2. Divide 676 by 2 to obtain the quotient (338).
676 ÷ 2 = 338
• Step 3. Repeat step 1 with the obtained quotient (338).
338 ÷ 2 = 169
169 ÷ 13 = 13
13 ÷ 13 = 1

So, the prime factorization of 676 is, 676 = 2 x 2 x 13 x 13.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 676 as shown below:

So, the prime factorization of 676 is, 676 = 2 x 2 x 13 x 13.

#### 3. Find factors of 676 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 676 would be the two numbers which, when multiplied, give 676 as the result.

The following table represents the calculation of factors of 676 in pairs:

Factor Pair Pair Factorization
1 and 676 1 x 676 = 676
2 and 338 2 x 338 = 676
4 and 169 4 x 169 = 676
13 and 52 13 x 52 = 676
26 and 26 26 x 26 = 676

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 676. They are called negative pair factors.

Hence, the negative pairs of 676 would be ( -1 , -676 ) , ( -2 , -338 ) , ( -4 , -169 ) , ( -13 , -52 ) and ( -26 , -26 ) .

#### How can we define factors?

In mathematics a factor is a number which divides into another without leaving any remainder. Or we can say, any two numbers that multiply to give a product are both factors of that product. It can be both positive or negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 676 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 676.
• Every number is a factor of zero (0), since 676 x 0 = 0.
• 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, 4, 13, 26, 52, 169, 338, 676 are exact divisors of 676.
• Factors of 676 are 1, 2, 4, 13, 26, 52, 169, 338, 676. Each factor divides 676 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 13, 26, 52, 169, 338, 676 are all less than or equal to 676.

• What are the prime factors of 676?

The factors of 676 are 1, 2, 4, 13, 26, 52, 169, 338, 676.
Prime factors of 676 are 2, 2, 13, 13.

• What is the sum of all factors of 676?

The sum of all factors of 676 is 1281.

• What are the pair factors of 676?

Pair factors of 676 are (1,676), (2,338), (4,169), (13,52), (26,26).

• What two numbers make 676?

Two numbers that make 676 are 2 and 338.

• What are multiples of 676?

First five multiples of 676 are 1352, 2028, 2704, 3380.

• Is 676 a perfect square?

Yes 676 is a perfect square.

• Which is greatest factor of 676?

The greatest factor of 676 is 338.

• How do you factors of 676?

Factors of 676 are 1, 2, 4, 13, 26, 52, 169, 338, 676.

• What are five multiples of 676?

First five multiples of 676 are 1352, 2028, 2704, 3380, 4056.

#### Examples of Factors

Can you help Rubel to find out the product of the even factors of 676?

Factors of 676 are 1, 2, 4, 13, 26, 52, 169, 338, 676.
Even factors of 676 are 2, 4, 26, 52, 338, 676.
Hence, product of even factors of 676 is; 2 x 4 x 26 x 52 x 338 x 676 = 2471326208.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 676? Help her in writing all the factors.

Positive factors are 1, 2, 4, 13, 26, 52, 169, 338, 676.
Negative factors are -1, -2, -4, -13, -26, -52, -169, -338, -676.

How many factors are there for 676?

Factors of 676 are 1, 2, 4, 13, 26, 52, 169, 338, 676.
So there are in total 9 factors.

Sammy is puzzled while calculating the prime factors of 676. Can you help him find them?

Factors of 676 are 1, 2, 4, 13, 26, 52, 169, 338, 676.
Prime factors of 676 are 2, 2, 13, 13

Joey wants to write all the prime factors of 676 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 676 are 2, 2, 13, 13.
So in exponential form it can be written as 22 x 132.

What is prime factorization of 676?

Prime factorization of 676 is 2 x 2 x 13 x 13 = 22 x 132.

Can you help Rubel to find out the product of the even factors of 676?

Factors of 676 are 1, 2, 4, 13, 26, 52, 169, 338, 676.
Even factors of 676 are 2, 4, 26, 52, 338, 676.
Hence, product of even factors of 676 is; 2 x 4 x 26 x 52 x 338 x 676 = 2471326208.