# Factors of 361

Factors of 361 are 1, 19, and 361

#### How to find factors of a number

 1.   Find factors of 361 using Division Method 2.   Find factors of 361 using Prime Factorization 3.   Find factors of 361 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 361

• Divide 361 by 1: 361 ÷ 1 : Remainder = 0
• Divide 361 by 19: 361 ÷ 19 : Remainder = 0
• Divide 361 by 361: 361 ÷ 361 : Remainder = 0

Hence, Factors of 361 are 1, 19, and 361

#### 2. Steps to find factors of 361 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 361 using the division method, follow these steps:

• Step 1. Start dividing 361 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 361, which is 19. Divide 361 by 19 to obtain the quotient (19).
361 ÷ 19 = 19
• Step 3. Repeat step 1 with the obtained quotient (19).
19 ÷ 19 = 1

So, the prime factorization of 361 is, 361 = 19 x 19.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 361 as shown below:

So, the prime factorization of 361 is, 361 = 19 x 19.

#### 3. Find factors of 361 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 361 would be the two numbers which, when multiplied, give 361 as the result.

The following table represents the calculation of factors of 361 in pairs:

Factor Pair Pair Factorization
1 and 361 1 x 361 = 361
19 and 19 19 x 19 = 361

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 361. They are called negative pair factors.

Hence, the negative pairs of 361 would be ( -1 , -361 ) , ( -19 , -19 ) .

#### 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

• Every factor of a number is an exact divisor of that number, example 1, 19, 361 are exact divisors of 361.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Each number is a factor of itself. Eg. 361 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 361.

• What are the prime factors of 361?

The factors of 361 are 1, 19, 361.
Prime factors of 361 are 19, 19.

• What is the sum of all factors of 361?

The sum of all factors of 361 is 381.

• What are the pair factors of 361?

Pair factors of 361 are (1,361), (19,19).

• What two numbers make 361?

Two numbers that make 361 are 19 and 19.

• What are multiples of 361?

First five multiples of 361 are 722, 1083, 1444, 1805.

• Is 361 a perfect square?

Yes 361 is a perfect square.

• Which is greatest factor of 361?

The greatest factor of 361 is 19.

• How do you factors of 361?

Factors of 361 are 1, 19, 361.

• What are five multiples of 361?

First five multiples of 361 are 722, 1083, 1444, 1805, 2166.

#### Examples of Factors

Can you help Rubel to find out the product of the even factors of 361?

Factors of 361 are 1, 19, 361.
Even factors of 361 are 0.
Hence, product of even factors of 361 is; 0 = 0.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 361? Help her in writing all the factors.

Positive factors are 1, 19, 361.
Negative factors are -1, -19, -361.

How many factors are there for 361?

Factors of 361 are 1, 19, 361.
So there are in total 3 factors.

Sammy is puzzled while calculating the prime factors of 361. Can you help him find them?

Factors of 361 are 1, 19, 361.
Prime factors of 361 are 19, 19

Joey wants to write all the prime factors of 361 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 361 are 19, 19.
So in exponential form it can be written as 192.

What is prime factorization of 361?

Prime factorization of 361 is 19 x 19 = 192.

Can you help Rubel to find out the product of the even factors of 361?

Factors of 361 are 1, 19, 361.
Even factors of 361 are 0.
Hence, product of even factors of 361 is; 0 = 0.