# Factors of 186

Factors of 186 are 1, 2, 3, 6, 31, 62, 93, and 186

#### How to find factors of a number

 1.   Find factors of 186 using Division Method 2.   Find factors of 186 using Prime Factorization 3.   Find factors of 186 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 186

• Divide 186 by 1: 186 ÷ 1 : Remainder = 0
• Divide 186 by 2: 186 ÷ 2 : Remainder = 0
• Divide 186 by 3: 186 ÷ 3 : Remainder = 0
• Divide 186 by 6: 186 ÷ 6 : Remainder = 0
• Divide 186 by 31: 186 ÷ 31 : Remainder = 0
• Divide 186 by 62: 186 ÷ 62 : Remainder = 0
• Divide 186 by 93: 186 ÷ 93 : Remainder = 0
• Divide 186 by 186: 186 ÷ 186 : Remainder = 0

Hence, Factors of 186 are 1, 2, 3, 6, 31, 62, 93, and 186

#### 2. Steps to find factors of 186 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 186 using the division method, follow these steps:

• Step 1. Start dividing 186 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 186, which is 2. Divide 186 by 2 to obtain the quotient (93).
186 ÷ 2 = 93
• Step 3. Repeat step 1 with the obtained quotient (93).
93 ÷ 3 = 31
31 ÷ 31 = 1

So, the prime factorization of 186 is, 186 = 2 x 3 x 31.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 186 as shown below:

So, the prime factorization of 186 is, 186 = 2 x 3 x 31.

#### 3. Find factors of 186 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 186 would be the two numbers which, when multiplied, give 186 as the result.

The following table represents the calculation of factors of 186 in pairs:

Factor Pair Pair Factorization
1 and 186 1 x 186 = 186
2 and 93 2 x 93 = 186
3 and 62 3 x 62 = 186
6 and 31 6 x 31 = 186

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 186. They are called negative pair factors.

Hence, the negative pairs of 186 would be ( -1 , -186 ) , ( -2 , -93 ) , ( -3 , -62 ) and ( -6 , -31 ) .

#### 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. 186 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, 31, 62, 93, 186 are exact divisors of 186.
• 1 is a factor of every number. Eg. 1 is a factor of 186.
• Every number is a factor of zero (0), since 186 x 0 = 0.

• How do you find factors of a negative number? ( eg. -186 )?

Factors of -186 are -1, -2, -3, -6, -31, -62, -93, -186.

• What is the sum of all factors of 186?

The sum of all factors of 186 is 384.

• What is prime factorization of 186?

Prime factorization of 186 is 2 x 3 x 31.

• What are the pair factors of 186?

Pair factors of 186 are (1,186), (2,93), (3,62), (6,31).

• What are six multiples of 186?

First five multiples of 186 are 372, 558, 744, 930, 1116, 1302.

• Is 186 a whole number?

Yes 186 is a whole number.

• Which is the smallest prime factor of 186?

Smallest prime factor of 186 is 2.

• What are five multiples of 186?

First five multiples of 186 are 372, 558, 744, 930, 1116.

• Write all factors of 186?

Factors of 186 are 1, 2, 3, 6, 31, 62, 93, 186.

#### Examples of Factors

Joey wants to write all the prime factors of 186 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 186 are 2, 3, 31.
So in exponential form it can be written as 2 x 3 x 31.

How many factors are there for 186?

Factors of 186 are 1, 2, 3, 6, 31, 62, 93, 186.
So there are in total 8 factors.

Kevin has been asked to write 7 factor(s) of 186. Can you predict the answer?

7 factor(s) of 186 are 1, 2, 3, 6, 31, 62, 93.

Sammy is puzzled while calculating the prime factors of 186. Can you help him find them?

Factors of 186 are 1, 2, 3, 6, 31, 62, 93, 186.
Prime factors of 186 are 2, 3, 31

What is prime factorization of 186?

Prime factorization of 186 is 2 x 3 x 31 = 2 x 3 x 31.

Ariel has been assigned the task to find the product of all the prime factors of 186. Can you help her?

Prime factors of 186 are 2, 3, 31.
Hence, the product of prime factors of 186.

Can you help Rubel to find out the product of the even factors of 186?

Factors of 186 are 1, 2, 3, 6, 31, 62, 93, 186.
Even factors of 186 are 2, 6, 62, 186.
Hence, product of even factors of 186 is; 2 x 6 x 62 x 186 = 138384.