# Factors of 357

Factors of 357 are 1, 3, 7, 17, 21, 51, 119, and 357

#### How to find factors of a number

 1.   Find factors of 357 using Division Method 2.   Find factors of 357 using Prime Factorization 3.   Find factors of 357 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 357

• Divide 357 by 1: 357 ÷ 1 : Remainder = 0
• Divide 357 by 3: 357 ÷ 3 : Remainder = 0
• Divide 357 by 7: 357 ÷ 7 : Remainder = 0
• Divide 357 by 17: 357 ÷ 17 : Remainder = 0
• Divide 357 by 21: 357 ÷ 21 : Remainder = 0
• Divide 357 by 51: 357 ÷ 51 : Remainder = 0
• Divide 357 by 119: 357 ÷ 119 : Remainder = 0
• Divide 357 by 357: 357 ÷ 357 : Remainder = 0

Hence, Factors of 357 are 1, 3, 7, 17, 21, 51, 119, and 357

#### 2. Steps to find factors of 357 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 357 using the division method, follow these steps:

• Step 1. Start dividing 357 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 357, which is 3. Divide 357 by 3 to obtain the quotient (119).
357 ÷ 3 = 119
• Step 3. Repeat step 1 with the obtained quotient (119).
119 ÷ 7 = 17
17 ÷ 17 = 1

So, the prime factorization of 357 is, 357 = 3 x 7 x 17.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 357 as shown below:

So, the prime factorization of 357 is, 357 = 3 x 7 x 17.

#### 3. Find factors of 357 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 357 would be the two numbers which, when multiplied, give 357 as the result.

The following table represents the calculation of factors of 357 in pairs:

Factor Pair Pair Factorization
1 and 357 1 x 357 = 357
3 and 119 3 x 119 = 357
7 and 51 7 x 51 = 357
17 and 21 17 x 21 = 357

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 357. They are called negative pair factors.

Hence, the negative pairs of 357 would be ( -1 , -357 ) , ( -3 , -119 ) , ( -7 , -51 ) and ( -17 , -21 ) .

#### How do you explain factors?

In mathematics, a factor is a number or also it can be an algebraic expression that divides another number or any expression completely and that too without leaving any remainder. A factor of a number can be positive or negative.

#### Properties of factors

• Every factor of a number is an exact divisor of that number, example 1, 3, 7, 17, 21, 51, 119, 357 are exact divisors of 357.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Each number is a factor of itself. Eg. 357 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 357.

• How do you find factors of a negative number? ( eg. -357 )?

Factors of -357 are -1, -3, -7, -17, -21, -51, -119, -357.

• What is the sum of all factors of 357?

The sum of all factors of 357 is 576.

• What is prime factorization of 357?

Prime factorization of 357 is 3 x 7 x 17.

• What are the pair factors of 357?

Pair factors of 357 are (1,357), (3,119), (7,51), (17,21).

• What are six multiples of 357?

First five multiples of 357 are 714, 1071, 1428, 1785, 2142, 2499.

• Is 357 a whole number?

Yes 357 is a whole number.

• Which is the smallest prime factor of 357?

Smallest prime factor of 357 is 3.

• What are five multiples of 357?

First five multiples of 357 are 714, 1071, 1428, 1785, 2142.

• Write all factors of 357?

Factors of 357 are 1, 3, 7, 17, 21, 51, 119, 357.

#### Examples of Factors

Joey wants to write all the prime factors of 357 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 357 are 3, 7, 17.
So in exponential form it can be written as 3 x 7 x 17.

How many factors are there for 357?

Factors of 357 are 1, 3, 7, 17, 21, 51, 119, 357.
So there are in total 8 factors.

Kevin has been asked to write 7 factor(s) of 357. Can you predict the answer?

7 factor(s) of 357 are 1, 3, 7, 17, 21, 51, 119.

Sammy is puzzled while calculating the prime factors of 357. Can you help him find them?

Factors of 357 are 1, 3, 7, 17, 21, 51, 119, 357.
Prime factors of 357 are 3, 7, 17

What is prime factorization of 357?

Prime factorization of 357 is 3 x 7 x 17 = 3 x 7 x 17.

Ariel has been assigned the task to find the product of all the prime factors of 357. Can you help her?

Prime factors of 357 are 3, 7, 17.
Hence, the product of prime factors of 357.

Can you help Rubel to find out the product of the even factors of 357?

Factors of 357 are 1, 3, 7, 17, 21, 51, 119, 357.
Even factors of 357 are 0.
Hence, product of even factors of 357 is; 0 = 0.