# Factors of 102

Factors of 102 are 1, 2, 3, 6, 17, 34, 51, and 102

#### How to find factors of a number

 1.   Find factors of 102 using Division Method 2.   Find factors of 102 using Prime Factorization 3.   Find factors of 102 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 102

• Divide 102 by 1: 102 ÷ 1 : Remainder = 0
• Divide 102 by 2: 102 ÷ 2 : Remainder = 0
• Divide 102 by 3: 102 ÷ 3 : Remainder = 0
• Divide 102 by 6: 102 ÷ 6 : Remainder = 0
• Divide 102 by 17: 102 ÷ 17 : Remainder = 0
• Divide 102 by 34: 102 ÷ 34 : Remainder = 0
• Divide 102 by 51: 102 ÷ 51 : Remainder = 0
• Divide 102 by 102: 102 ÷ 102 : Remainder = 0

Hence, Factors of 102 are 1, 2, 3, 6, 17, 34, 51, and 102

#### 2. Steps to find factors of 102 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 102 using the division method, follow these steps:

• Step 1. Start dividing 102 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 102, which is 2. Divide 102 by 2 to obtain the quotient (51).
102 ÷ 2 = 51
• Step 3. Repeat step 1 with the obtained quotient (51).
51 ÷ 3 = 17
17 ÷ 17 = 1

So, the prime factorization of 102 is, 102 = 2 x 3 x 17.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 102 as shown below:

So, the prime factorization of 102 is, 102 = 2 x 3 x 17.

#### 3. Find factors of 102 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 102 would be the two numbers which, when multiplied, give 102 as the result.

The following table represents the calculation of factors of 102 in pairs:

Factor Pair Pair Factorization
1 and 102 1 x 102 = 102
2 and 51 2 x 51 = 102
3 and 34 3 x 34 = 102
6 and 17 6 x 17 = 102

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 102. They are called negative pair factors.

Hence, the negative pairs of 102 would be ( -1 , -102 ) , ( -2 , -51 ) , ( -3 , -34 ) and ( -6 , -17 ) .

#### 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

• Each number is a factor of itself. Eg. 102 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, 17, 34, 51, 102 are exact divisors of 102.
• 1 is a factor of every number. Eg. 1 is a factor of 102.
• Every number is a factor of zero (0), since 102 x 0 = 0.

• What are the prime factors of 102?

The factors of 102 are 1, 2, 3, 6, 17, 34, 51, 102.
Prime factors of 102 are 2, 3, 17.

• What two numbers make 102?

Two numbers that make 102 are 2 and 51.

• What is the greatest prime factors of 102?

The greatest prime factor of 102 is 17.

• What are factors of 102?

Factors of 102 are 1, 2, 3, 6, 17, 34, 51, 102.

• How do you find factors of a negative number? ( eg. -102 )?

Factors of -102 are -1, -2, -3, -6, -17, -34, -51, -102.

• What are five multiples of 102?

First five multiples of 102 are 204, 306, 408, 510, 612.

• Write some multiples of 102?

First five multiples of 102 are 204, 306, 408, 510.

• Is 102 a perfect square?

No 102 is not a perfect square.

• What two numbers make 102?

Two numbers that make 102 are 2 and 51.

#### Examples of Factors

What is prime factorization of 102?

Prime factorization of 102 is 2 x 3 x 17 = 2 x 3 x 17.

Sammy is puzzled while calculating the prime factors of 102. Can you help him find them?

Factors of 102 are 1, 2, 3, 6, 17, 34, 51, 102.
Prime factors of 102 are 2, 3, 17

Kevin has been asked to write 7 factor(s) of 102. Can you predict the answer?

7 factor(s) of 102 are 1, 2, 3, 6, 17, 34, 51.

Joey wants to write all the prime factors of 102 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 102 are 2, 3, 17.
So in exponential form it can be written as 2 x 3 x 17.

How many factors are there for 102?

Factors of 102 are 1, 2, 3, 6, 17, 34, 51, 102.
So there are in total 8 factors.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 102? Help her in writing all the factors.

Positive factors are 1, 2, 3, 6, 17, 34, 51, 102.
Negative factors are -1, -2, -3, -6, -17, -34, -51, -102.

Can you help Rubel to find out the product of the even factors of 102?

Factors of 102 are 1, 2, 3, 6, 17, 34, 51, 102.
Even factors of 102 are 2, 6, 34, 102.
Hence, product of even factors of 102 is; 2 x 6 x 34 x 102 = 41616.