# Factors of 234

Factors of 234 are 1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117, and 234

#### How to find factors of a number

 1.   Find factors of 234 using Division Method 2.   Find factors of 234 using Prime Factorization 3.   Find factors of 234 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 234

• Divide 234 by 1: 234 ÷ 1 : Remainder = 0
• Divide 234 by 2: 234 ÷ 2 : Remainder = 0
• Divide 234 by 3: 234 ÷ 3 : Remainder = 0
• Divide 234 by 6: 234 ÷ 6 : Remainder = 0
• Divide 234 by 9: 234 ÷ 9 : Remainder = 0
• Divide 234 by 13: 234 ÷ 13 : Remainder = 0
• Divide 234 by 18: 234 ÷ 18 : Remainder = 0
• Divide 234 by 26: 234 ÷ 26 : Remainder = 0
• Divide 234 by 39: 234 ÷ 39 : Remainder = 0
• Divide 234 by 78: 234 ÷ 78 : Remainder = 0
• Divide 234 by 117: 234 ÷ 117 : Remainder = 0
• Divide 234 by 234: 234 ÷ 234 : Remainder = 0

Hence, Factors of 234 are 1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117, and 234

#### 2. Steps to find factors of 234 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 234 using the division method, follow these steps:

• Step 1. Start dividing 234 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 234, which is 2. Divide 234 by 2 to obtain the quotient (117).
234 ÷ 2 = 117
• Step 3. Repeat step 1 with the obtained quotient (117).
117 ÷ 3 = 39
39 ÷ 3 = 13
13 ÷ 13 = 1

So, the prime factorization of 234 is, 234 = 2 x 3 x 3 x 13.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 234 as shown below:

So, the prime factorization of 234 is, 234 = 2 x 3 x 3 x 13.

#### 3. Find factors of 234 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 234 would be the two numbers which, when multiplied, give 234 as the result.

The following table represents the calculation of factors of 234 in pairs:

Factor Pair Pair Factorization
1 and 234 1 x 234 = 234
2 and 117 2 x 117 = 234
3 and 78 3 x 78 = 234
6 and 39 6 x 39 = 234
9 and 26 9 x 26 = 234
13 and 18 13 x 18 = 234

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 234. They are called negative pair factors.

Hence, the negative pairs of 234 would be ( -1 , -234 ) , ( -2 , -117 ) , ( -3 , -78 ) , ( -6 , -39 ) , ( -9 , -26 ) and ( -13 , -18 ) .

#### 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. 234 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, 13, 18, 26, 39, 78, 117, 234 are exact divisors of 234.
• 1 is a factor of every number. Eg. 1 is a factor of 234.
• Every number is a factor of zero (0), since 234 x 0 = 0.

• Which is the smallest prime factor of 234?

Smallest prime factor of 234 is 2.

• Is 234 a perfect square?

No 234 is not a perfect square.

• What are five multiples of 234?

First five multiples of 234 are 468, 702, 936, 1170, 1404.

• What is prime factorization of 234?

Prime factorization of 234 is 2 x 3 x 3 x 13.

• What are factors of 234?

Factors of 234 are 1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117, 234.

• How do you find factors of a negative number? ( eg. -234 )?

Factors of -234 are -1, -2, -3, -6, -9, -13, -18, -26, -39, -78, -117, -234.

• Is 234 a whole number?

Yes 234 is a whole number.

• Which is greatest factor of 234?

The greatest factor of 234 is 117.

• What are the prime factors of 234?

The factors of 234 are 1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117, 234.
Prime factors of 234 are 2, 3, 3, 13.

#### Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 234. Can you help her?

Prime factors of 234 are 2, 3, 3, 13.
Hence, the product of prime factors of 78.

Can you help Rubel to find out the product of the even factors of 234?

Factors of 234 are 1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117, 234.
Even factors of 234 are 2, 6, 18, 26, 78, 234.
Hence, product of even factors of 234 is; 2 x 6 x 18 x 26 x 78 x 234 = 102503232.

Joy wants to calculate mean of all the factors of 234. Help him in finding the mean of 234.

Factors of 234 are 1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117, 234.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 234 is 1 + 2 + 3 + 6 + 9 + 13 + 18 + 26 + 39 + 78 + 117 + 234 = 546.
Hence, the mean of factors of 234 is 546 ÷ 12 = 45.50.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 234? Help her in writing all the factors.

Positive factors are 1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117, 234.
Negative factors are -1, -2, -3, -6, -9, -13, -18, -26, -39, -78, -117, -234.

How many factors are there for 234?

Factors of 234 are 1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117, 234.
So there are in total 12 factors.

Joey wants to write all the prime factors of 234 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 234 are 2, 3, 3, 13.
So in exponential form it can be written as 2 x 32 x 13.

Kevin has been asked to write 11 factor(s) of 234. Can you predict the answer?

11 factor(s) of 234 are 1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117.