# Factors of 666

Factors of 666 are 1, 2, 3, 6, 9, 18, 37, 74, 111, 222, 333, and 666

#### How to find factors of a number

 1.   Find factors of 666 using Division Method 2.   Find factors of 666 using Prime Factorization 3.   Find factors of 666 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 666

• Divide 666 by 1: 666 ÷ 1 : Remainder = 0
• Divide 666 by 2: 666 ÷ 2 : Remainder = 0
• Divide 666 by 3: 666 ÷ 3 : Remainder = 0
• Divide 666 by 6: 666 ÷ 6 : Remainder = 0
• Divide 666 by 9: 666 ÷ 9 : Remainder = 0
• Divide 666 by 18: 666 ÷ 18 : Remainder = 0
• Divide 666 by 37: 666 ÷ 37 : Remainder = 0
• Divide 666 by 74: 666 ÷ 74 : Remainder = 0
• Divide 666 by 111: 666 ÷ 111 : Remainder = 0
• Divide 666 by 222: 666 ÷ 222 : Remainder = 0
• Divide 666 by 333: 666 ÷ 333 : Remainder = 0
• Divide 666 by 666: 666 ÷ 666 : Remainder = 0

Hence, Factors of 666 are 1, 2, 3, 6, 9, 18, 37, 74, 111, 222, 333, and 666

#### 2. Steps to find factors of 666 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 666 using the division method, follow these steps:

• Step 1. Start dividing 666 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 666, which is 2. Divide 666 by 2 to obtain the quotient (333).
666 ÷ 2 = 333
• Step 3. Repeat step 1 with the obtained quotient (333).
333 ÷ 3 = 111
111 ÷ 3 = 37
37 ÷ 37 = 1

So, the prime factorization of 666 is, 666 = 2 x 3 x 3 x 37.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 666 as shown below:

So, the prime factorization of 666 is, 666 = 2 x 3 x 3 x 37.

#### 3. Find factors of 666 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 666 would be the two numbers which, when multiplied, give 666 as the result.

The following table represents the calculation of factors of 666 in pairs:

Factor Pair Pair Factorization
1 and 666 1 x 666 = 666
2 and 333 2 x 333 = 666
3 and 222 3 x 222 = 666
6 and 111 6 x 111 = 666
9 and 74 9 x 74 = 666
18 and 37 18 x 37 = 666

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 666. They are called negative pair factors.

Hence, the negative pairs of 666 would be ( -1 , -666 ) , ( -2 , -333 ) , ( -3 , -222 ) , ( -6 , -111 ) , ( -9 , -74 ) and ( -18 , -37 ) .

#### 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

• Each number is a factor of itself. Eg. 666 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, 9, 18, 37, 74, 111, 222, 333, 666 are exact divisors of 666.
• 1 is a factor of every number. Eg. 1 is a factor of 666.
• Every number is a factor of zero (0), since 666 x 0 = 0.

• Which is the smallest prime factor of 666?

Smallest prime factor of 666 is 2.

• Is 666 a perfect square?

No 666 is not a perfect square.

• What are five multiples of 666?

First five multiples of 666 are 1332, 1998, 2664, 3330, 3996.

• What is prime factorization of 666?

Prime factorization of 666 is 2 x 3 x 3 x 37.

• What are factors of 666?

Factors of 666 are 1, 2, 3, 6, 9, 18, 37, 74, 111, 222, 333, 666.

• How do you find factors of a negative number? ( eg. -666 )?

Factors of -666 are -1, -2, -3, -6, -9, -18, -37, -74, -111, -222, -333, -666.

• Is 666 a whole number?

Yes 666 is a whole number.

• Which is greatest factor of 666?

The greatest factor of 666 is 333.

• What are the prime factors of 666?

The factors of 666 are 1, 2, 3, 6, 9, 18, 37, 74, 111, 222, 333, 666.
Prime factors of 666 are 2, 3, 3, 37.

#### Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 666. Can you help her?

Prime factors of 666 are 2, 3, 3, 37.
Hence, the product of prime factors of 222.

Can you help Rubel to find out the product of the even factors of 666?

Factors of 666 are 1, 2, 3, 6, 9, 18, 37, 74, 111, 222, 333, 666.
Even factors of 666 are 2, 6, 18, 74, 222, 666.
Hence, product of even factors of 666 is; 2 x 6 x 18 x 74 x 222 x 666 = 2363266368.

Joy wants to calculate mean of all the factors of 666. Help him in finding the mean of 666.

Factors of 666 are 1, 2, 3, 6, 9, 18, 37, 74, 111, 222, 333, 666.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 666 is 1 + 2 + 3 + 6 + 9 + 18 + 37 + 74 + 111 + 222 + 333 + 666 = 1482.
Hence, the mean of factors of 666 is 1482 ÷ 12 = 123.50.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 666? Help her in writing all the factors.

Positive factors are 1, 2, 3, 6, 9, 18, 37, 74, 111, 222, 333, 666.
Negative factors are -1, -2, -3, -6, -9, -18, -37, -74, -111, -222, -333, -666.

How many factors are there for 666?

Factors of 666 are 1, 2, 3, 6, 9, 18, 37, 74, 111, 222, 333, 666.
So there are in total 12 factors.

Joey wants to write all the prime factors of 666 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 666 are 2, 3, 3, 37.
So in exponential form it can be written as 2 x 32 x 37.

Kevin has been asked to write 11 factor(s) of 666. Can you predict the answer?

11 factor(s) of 666 are 1, 2, 3, 6, 9, 18, 37, 74, 111, 222, 333.