# Factors of 364

Factors of 364 are 1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182, and 364

#### How to find factors of a number

 1.   Find factors of 364 using Division Method 2.   Find factors of 364 using Prime Factorization 3.   Find factors of 364 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 364

• Divide 364 by 1: 364 ÷ 1 : Remainder = 0
• Divide 364 by 2: 364 ÷ 2 : Remainder = 0
• Divide 364 by 4: 364 ÷ 4 : Remainder = 0
• Divide 364 by 7: 364 ÷ 7 : Remainder = 0
• Divide 364 by 13: 364 ÷ 13 : Remainder = 0
• Divide 364 by 14: 364 ÷ 14 : Remainder = 0
• Divide 364 by 26: 364 ÷ 26 : Remainder = 0
• Divide 364 by 28: 364 ÷ 28 : Remainder = 0
• Divide 364 by 52: 364 ÷ 52 : Remainder = 0
• Divide 364 by 91: 364 ÷ 91 : Remainder = 0
• Divide 364 by 182: 364 ÷ 182 : Remainder = 0
• Divide 364 by 364: 364 ÷ 364 : Remainder = 0

Hence, Factors of 364 are 1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182, and 364

#### 2. Steps to find factors of 364 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 364 using the division method, follow these steps:

• Step 1. Start dividing 364 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 364, which is 2. Divide 364 by 2 to obtain the quotient (182).
364 ÷ 2 = 182
• Step 3. Repeat step 1 with the obtained quotient (182).
182 ÷ 2 = 91
91 ÷ 7 = 13
13 ÷ 13 = 1

So, the prime factorization of 364 is, 364 = 2 x 2 x 7 x 13.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 364 as shown below:

So, the prime factorization of 364 is, 364 = 2 x 2 x 7 x 13.

#### 3. Find factors of 364 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 364 would be the two numbers which, when multiplied, give 364 as the result.

The following table represents the calculation of factors of 364 in pairs:

Factor Pair Pair Factorization
1 and 364 1 x 364 = 364
2 and 182 2 x 182 = 364
4 and 91 4 x 91 = 364
7 and 52 7 x 52 = 364
13 and 28 13 x 28 = 364
14 and 26 14 x 26 = 364

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 364. They are called negative pair factors.

Hence, the negative pairs of 364 would be ( -1 , -364 ) , ( -2 , -182 ) , ( -4 , -91 ) , ( -7 , -52 ) , ( -13 , -28 ) and ( -14 , -26 ) .

#### How can we define factors?

In mathematics, a factor is a number which divides into another number exactly, without leaving any remainder. A factor of a number can be positive of negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 364 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 364.
• Every number is a factor of zero (0), since 364 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, 7, 13, 14, 26, 28, 52, 91, 182, 364 are exact divisors of 364.
• Factors of 364 are 1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182, 364. Each factor divides 364 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182, 364 are all less than or equal to 364.

• Is 364 a perfect square?

No 364 is not a perfect square.

• What are factors of 364?

Factors of 364 are 1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182, 364.

• Which is greatest factor of 364?

The greatest factor of 364 is 182.

• What is the sum of all factors of 364?

The sum of all factors of 364 is 784.

• What are multiples of 364?

First five multiples of 364 are 728, 1092, 1456, 1820.

• What is the greatest prime factors of 364?

The greatest prime factor of 364 is 13.

• What are six multiples of 364?

First five multiples of 364 are 728, 1092, 1456, 1820, 2184, 2548.

• What is prime factorization of 364?

Prime factorization of 364 is 2 x 2 x 7 x 13.

• Is 364 a whole number?

Yes 364 is a whole number.

#### Examples of Factors

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 364? Help her in writing all the factors.

Positive factors are 1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182, 364.
Negative factors are -1, -2, -4, -7, -13, -14, -26, -28, -52, -91, -182, -364.

Can you help Sammy find out the product of the odd factors of 364?

Factors of 364 are 1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182, 364.
Odd factors of 364 are 1, 7, 13, 91.
Hence product of odd factors of 364 is; 1 x 7 x 13 x 91 = 8281.

Joey wants to write all the prime factors of 364 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 364 are 2, 2, 7, 13.
So in exponential form it can be written as 22 x 7 x 13.

How many factors are there for 364?

Factors of 364 are 1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182, 364.
So there are in total 12 factors.

Kevin has been asked to write 11 factor(s) of 364. Can you predict the answer?

11 factor(s) of 364 are 1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182.

Sammy is puzzled while calculating the prime factors of 364. Can you help him find them?

Factors of 364 are 1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182, 364.
Prime factors of 364 are 2, 2, 7, 13

What is prime factorization of 364?

Prime factorization of 364 is 2 x 2 x 7 x 13 = 22 x 7 x 13.