# Factors of 654

Factors of 654 are 1, 2, 3, 6, 109, 218, 327, and 654

#### How to find factors of a number

 1.   Find factors of 654 using Division Method 2.   Find factors of 654 using Prime Factorization 3.   Find factors of 654 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 654

• Divide 654 by 1: 654 ÷ 1 : Remainder = 0
• Divide 654 by 2: 654 ÷ 2 : Remainder = 0
• Divide 654 by 3: 654 ÷ 3 : Remainder = 0
• Divide 654 by 6: 654 ÷ 6 : Remainder = 0
• Divide 654 by 109: 654 ÷ 109 : Remainder = 0
• Divide 654 by 218: 654 ÷ 218 : Remainder = 0
• Divide 654 by 327: 654 ÷ 327 : Remainder = 0
• Divide 654 by 654: 654 ÷ 654 : Remainder = 0

Hence, Factors of 654 are 1, 2, 3, 6, 109, 218, 327, and 654

#### 2. Steps to find factors of 654 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 654 using the division method, follow these steps:

• Step 1. Start dividing 654 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 654, which is 2. Divide 654 by 2 to obtain the quotient (327).
654 ÷ 2 = 327
• Step 3. Repeat step 1 with the obtained quotient (327).
327 ÷ 3 = 109
109 ÷ 109 = 1

So, the prime factorization of 654 is, 654 = 2 x 3 x 109.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 654 as shown below:

So, the prime factorization of 654 is, 654 = 2 x 3 x 109.

#### 3. Find factors of 654 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 654 would be the two numbers which, when multiplied, give 654 as the result.

The following table represents the calculation of factors of 654 in pairs:

Factor Pair Pair Factorization
1 and 654 1 x 654 = 654
2 and 327 2 x 327 = 654
3 and 218 3 x 218 = 654
6 and 109 6 x 109 = 654

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 654. They are called negative pair factors.

Hence, the negative pairs of 654 would be ( -1 , -654 ) , ( -2 , -327 ) , ( -3 , -218 ) and ( -6 , -109 ) .

#### 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. 654 is a factor of itself.
• 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, 3, 6, 109, 218, 327, 654 are exact divisors of 654.
• 1 is a factor of every number. Eg. 1 is a factor of 654.
• Every number is a factor of zero (0), since 654 x 0 = 0.

• How do you find factors of a negative number? ( eg. -654 )?

Factors of -654 are -1, -2, -3, -6, -109, -218, -327, -654.

• What is the sum of all factors of 654?

The sum of all factors of 654 is 1320.

• What is prime factorization of 654?

Prime factorization of 654 is 2 x 3 x 109.

• What are the pair factors of 654?

Pair factors of 654 are (1,654), (2,327), (3,218), (6,109).

• What are six multiples of 654?

First five multiples of 654 are 1308, 1962, 2616, 3270, 3924, 4578.

• Is 654 a whole number?

Yes 654 is a whole number.

• Which is the smallest prime factor of 654?

Smallest prime factor of 654 is 2.

• What are five multiples of 654?

First five multiples of 654 are 1308, 1962, 2616, 3270, 3924.

• Write all factors of 654?

Factors of 654 are 1, 2, 3, 6, 109, 218, 327, 654.

#### Examples of Factors

Joey wants to write all the prime factors of 654 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 654 are 2, 3, 109.
So in exponential form it can be written as 2 x 3 x 109.

How many factors are there for 654?

Factors of 654 are 1, 2, 3, 6, 109, 218, 327, 654.
So there are in total 8 factors.

Kevin has been asked to write 7 factor(s) of 654. Can you predict the answer?

7 factor(s) of 654 are 1, 2, 3, 6, 109, 218, 327.

Sammy is puzzled while calculating the prime factors of 654. Can you help him find them?

Factors of 654 are 1, 2, 3, 6, 109, 218, 327, 654.
Prime factors of 654 are 2, 3, 109

What is prime factorization of 654?

Prime factorization of 654 is 2 x 3 x 109 = 2 x 3 x 109.

Ariel has been assigned the task to find the product of all the prime factors of 654. Can you help her?

Prime factors of 654 are 2, 3, 109.
Hence, the product of prime factors of 654.

Can you help Rubel to find out the product of the even factors of 654?

Factors of 654 are 1, 2, 3, 6, 109, 218, 327, 654.
Even factors of 654 are 2, 6, 218, 654.
Hence, product of even factors of 654 is; 2 x 6 x 218 x 654 = 1710864.