# Factors of 657

Factors of 657 are 1, 3, 9, 73, 219, and 657

#### How to find factors of a number

 1.   Find factors of 657 using Division Method 2.   Find factors of 657 using Prime Factorization 3.   Find factors of 657 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 657

• Divide 657 by 1: 657 ÷ 1 : Remainder = 0
• Divide 657 by 3: 657 ÷ 3 : Remainder = 0
• Divide 657 by 9: 657 ÷ 9 : Remainder = 0
• Divide 657 by 73: 657 ÷ 73 : Remainder = 0
• Divide 657 by 219: 657 ÷ 219 : Remainder = 0
• Divide 657 by 657: 657 ÷ 657 : Remainder = 0

Hence, Factors of 657 are 1, 3, 9, 73, 219, and 657

#### 2. Steps to find factors of 657 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 657 using the division method, follow these steps:

• Step 1. Start dividing 657 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 657, which is 3. Divide 657 by 3 to obtain the quotient (219).
657 ÷ 3 = 219
• Step 3. Repeat step 1 with the obtained quotient (219).
219 ÷ 3 = 73
73 ÷ 73 = 1

So, the prime factorization of 657 is, 657 = 3 x 3 x 73.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 657 as shown below:

So, the prime factorization of 657 is, 657 = 3 x 3 x 73.

#### 3. Find factors of 657 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 657 would be the two numbers which, when multiplied, give 657 as the result.

The following table represents the calculation of factors of 657 in pairs:

Factor Pair Pair Factorization
1 and 657 1 x 657 = 657
3 and 219 3 x 219 = 657
9 and 73 9 x 73 = 657

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 657. They are called negative pair factors.

Hence, the negative pairs of 657 would be ( -1 , -657 ) , ( -3 , -219 ) and ( -9 , -73 ) .

#### 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, 9, 73, 219, 657 are exact divisors of 657.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Each number is a factor of itself. Eg. 657 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 657.

• Which is the smallest prime factor of 657?

Smallest prime factor of 657 is 3.

• Is 657 a perfect square?

No 657 is not a perfect square.

• What are five multiples of 657?

First five multiples of 657 are 1314, 1971, 2628, 3285, 3942.

• What is prime factorization of 657?

Prime factorization of 657 is 3 x 3 x 73.

• What are factors of 657?

Factors of 657 are 1, 3, 9, 73, 219, 657.

• How do you find factors of a negative number? ( eg. -657 )?

Factors of -657 are -1, -3, -9, -73, -219, -657.

• Is 657 a whole number?

Yes 657 is a whole number.

• Which is greatest factor of 657?

The greatest factor of 657 is 219.

• What are the prime factors of 657?

The factors of 657 are 1, 3, 9, 73, 219, 657.
Prime factors of 657 are 3, 3, 73.

#### Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 657. Can you help her?

Prime factors of 657 are 3, 3, 73.
Hence, the product of prime factors of 219.

Can you help Rubel to find out the product of the even factors of 657?

Factors of 657 are 1, 3, 9, 73, 219, 657.
Even factors of 657 are 0.
Hence, product of even factors of 657 is; 0 = 0.

Joy wants to calculate mean of all the factors of 657. Help him in finding the mean of 657.

Factors of 657 are 1, 3, 9, 73, 219, 657.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 657 is 1 + 3 + 9 + 73 + 219 + 657 = 962.
Hence, the mean of factors of 657 is 962 ÷ 6 = 160.33.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 657? Help her in writing all the factors.

Positive factors are 1, 3, 9, 73, 219, 657.
Negative factors are -1, -3, -9, -73, -219, -657.

How many factors are there for 657?

Factors of 657 are 1, 3, 9, 73, 219, 657.
So there are in total 6 factors.

Joey wants to write all the prime factors of 657 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 657 are 3, 3, 73.
So in exponential form it can be written as 32 x 73.

Kevin has been asked to write 5 factor(s) of 657. Can you predict the answer?

5 factor(s) of 657 are 1, 3, 9, 73, 219.