# Factors of 363

Factors of 363 are 1, 3, 11, 33, 121, and 363

#### How to find factors of a number

 1.   Find factors of 363 using Division Method 2.   Find factors of 363 using Prime Factorization 3.   Find factors of 363 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 363

• Divide 363 by 1: 363 ÷ 1 : Remainder = 0
• Divide 363 by 3: 363 ÷ 3 : Remainder = 0
• Divide 363 by 11: 363 ÷ 11 : Remainder = 0
• Divide 363 by 33: 363 ÷ 33 : Remainder = 0
• Divide 363 by 121: 363 ÷ 121 : Remainder = 0
• Divide 363 by 363: 363 ÷ 363 : Remainder = 0

Hence, Factors of 363 are 1, 3, 11, 33, 121, and 363

#### 2. Steps to find factors of 363 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 363 using the division method, follow these steps:

• Step 1. Start dividing 363 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 363, which is 3. Divide 363 by 3 to obtain the quotient (121).
363 ÷ 3 = 121
• Step 3. Repeat step 1 with the obtained quotient (121).
121 ÷ 11 = 11
11 ÷ 11 = 1

So, the prime factorization of 363 is, 363 = 3 x 11 x 11.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 363 as shown below:

So, the prime factorization of 363 is, 363 = 3 x 11 x 11.

#### 3. Find factors of 363 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 363 would be the two numbers which, when multiplied, give 363 as the result.

The following table represents the calculation of factors of 363 in pairs:

Factor Pair Pair Factorization
1 and 363 1 x 363 = 363
3 and 121 3 x 121 = 363
11 and 33 11 x 33 = 363

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 363. They are called negative pair factors.

Hence, the negative pairs of 363 would be ( -1 , -363 ) , ( -3 , -121 ) and ( -11 , -33 ) .

#### What is the definition of factors?

In mathematics, factors are number, algebraic expressions which when multiplied together produce desired product. A factor of a number can be positive or negative.

#### Properties of factors

• Every number is a factor of zero (0), since 363 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, 3, 11, 33, 121, 363 are exact divisors of 363.
• Factors of 363 are 1, 3, 11, 33, 121, 363. Each factor divides 363 without leaving a remainder.

• What are the prime factors of 363?

The factors of 363 are 1, 3, 11, 33, 121, 363.
Prime factors of 363 are 3, 11, 11.

• What two numbers make 363?

Two numbers that make 363 are 3 and 121.

• What is the greatest prime factors of 363?

The greatest prime factor of 363 is 11.

• What are factors of 363?

Factors of 363 are 1, 3, 11, 33, 121, 363.

• How do you find factors of a negative number? ( eg. -363 )?

Factors of -363 are -1, -3, -11, -33, -121, -363.

• What are five multiples of 363?

First five multiples of 363 are 726, 1089, 1452, 1815, 2178.

• Write some multiples of 363?

First five multiples of 363 are 726, 1089, 1452, 1815.

• Is 363 a perfect square?

No 363 is not a perfect square.

• What two numbers make 363?

Two numbers that make 363 are 3 and 121.

#### Examples of Factors

What is prime factorization of 363?

Prime factorization of 363 is 3 x 11 x 11 = 3 x 112.

Sammy is puzzled while calculating the prime factors of 363. Can you help him find them?

Factors of 363 are 1, 3, 11, 33, 121, 363.
Prime factors of 363 are 3, 11, 11

Kevin has been asked to write 5 factor(s) of 363. Can you predict the answer?

5 factor(s) of 363 are 1, 3, 11, 33, 121.

Joey wants to write all the prime factors of 363 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 363 are 3, 11, 11.
So in exponential form it can be written as 3 x 112.

How many factors are there for 363?

Factors of 363 are 1, 3, 11, 33, 121, 363.
So there are in total 6 factors.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 363? Help her in writing all the factors.

Positive factors are 1, 3, 11, 33, 121, 363.
Negative factors are -1, -3, -11, -33, -121, -363.

Can you help Rubel to find out the product of the even factors of 363?

Factors of 363 are 1, 3, 11, 33, 121, 363.
Even factors of 363 are 0.
Hence, product of even factors of 363 is; 0 = 0.