# Factors of 68

Factors of 68 are 1, 2, 4, 17, 34, and 68

#### How to find factors of a number

 1.   Find factors of 68 using Division Method 2.   Find factors of 68 using Prime Factorization 3.   Find factors of 68 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 68

• Divide 68 by 1: 68 ÷ 1 : Remainder = 0
• Divide 68 by 2: 68 ÷ 2 : Remainder = 0
• Divide 68 by 4: 68 ÷ 4 : Remainder = 0
• Divide 68 by 17: 68 ÷ 17 : Remainder = 0
• Divide 68 by 34: 68 ÷ 34 : Remainder = 0
• Divide 68 by 68: 68 ÷ 68 : Remainder = 0

Hence, Factors of 68 are 1, 2, 4, 17, 34, and 68

#### 2. Steps to find factors of 68 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 68 using the division method, follow these steps:

• Step 1. Start dividing 68 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 68, which is 2. Divide 68 by 2 to obtain the quotient (34).
68 ÷ 2 = 34
• Step 3. Repeat step 1 with the obtained quotient (34).
34 ÷ 2 = 17
17 ÷ 17 = 1

So, the prime factorization of 68 is, 68 = 2 x 2 x 17.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 68 as shown below:

So, the prime factorization of 68 is, 68 = 2 x 2 x 17.

#### 3. Find factors of 68 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 68 would be the two numbers which, when multiplied, give 68 as the result.

The following table represents the calculation of factors of 68 in pairs:

Factor Pair Pair Factorization
1 and 68 1 x 68 = 68
2 and 34 2 x 34 = 68
4 and 17 4 x 17 = 68

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 68. They are called negative pair factors.

Hence, the negative pairs of 68 would be ( -1 , -68 ) , ( -2 , -34 ) and ( -4 , -17 ) .

#### What is the definition of factors?

In mathematics, factors are number, algebraic expressions which when multiplied together produce desired product. A factor of a number can be positive or negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 68 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 68.
• Every number is a factor of zero (0), since 68 x 0 = 0.
• 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, 4, 17, 34, 68 are exact divisors of 68.
• Factors of 68 are 1, 2, 4, 17, 34, 68. Each factor divides 68 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 17, 34, 68 are all less than or equal to 68.

• What are the pair factors of 68?

Pair factors of 68 are (1,68), (2,34), (4,17).

• What are five multiples of 68?

First five multiples of 68 are 136, 204, 272, 340, 408.

• What two numbers make 68?

Two numbers that make 68 are 2 and 34.

• What is the sum of all factors of 68?

The sum of all factors of 68 is 126.

• What are factors of -68?

Factors of -68 are -1, -2, -4, -17, -34, -68.

• What are factors of 68?

Factors of 68 are 1, 2, 4, 17, 34, 68.

• Is 68 a perfect square?

No 68 is not a perfect square.

• Which is the smallest prime factor of 68?

Smallest prime factor of 68 is 2.

• Which is greatest factor of 68?

The greatest factor of 68 is 34.

#### Examples of Factors

Can you help Sammy find out the product of the odd factors of 68?

Factors of 68 are 1, 2, 4, 17, 34, 68.
Odd factors of 68 are 1, 17.
Hence product of odd factors of 68 is; 1 x 17 = 17.

Joey wants to write all the prime factors of 68 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 68 are 2, 2, 17.
So in exponential form it can be written as 22 x 17.

How many factors are there for 68?

Factors of 68 are 1, 2, 4, 17, 34, 68.
So there are in total 6 factors.

Kevin has been asked to write 5 factor(s) of 68. Can you predict the answer?

5 factor(s) of 68 are 1, 2, 4, 17, 34.

Sammy is puzzled while calculating the prime factors of 68. Can you help him find them?

Factors of 68 are 1, 2, 4, 17, 34, 68.
Prime factors of 68 are 2, 2, 17

What is prime factorization of 68?

Prime factorization of 68 is 2 x 2 x 17 = 22 x 17.

Can you help Rubel to find out the product of the even factors of 68?

Factors of 68 are 1, 2, 4, 17, 34, 68.
Even factors of 68 are 2, 4, 34, 68.
Hence, product of even factors of 68 is; 2 x 4 x 34 x 68 = 18496.