Factors of 234
Factors of 234 are the list of integers that we can split evenly into 234. There are overall 12 factors of 234, of which 2, 3, 13 are its prime factors. The sum of all factors of 234 is 546.
- All Factors of 234: 1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117 and 234
- Prime Factors of 234: 2, 3, 13
- Prime Factorization of 234: 21 × 32 × 131
- Sum of Factors of 234: 546
1. | What Are the Factors of 234? |
2. | Factors of 234 by Prime Factorization |
3. | Factors of 234 in Pairs |
4. | FAQs on Factors of 234 |

What are Factors of 234?
Factors of 234 are pairs of those numbers whose products result in 234. These factors are either prime numbers or composite numbers.
How to Find the Factors of 234?
To find the factors of 234, we will have to find the list of numbers that would divide 234 without leaving any remainder.
- 234/2 = 117; therefore, 2 is a factor of 234 and 117 is also a factor of 234.
- 234/18 = 13; therefore, 18 is a factor of 234 and 13 is also a factor of 234.
☛ Also Check:
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- Factors of 100 - The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, 100
- Factors of 20 - The factors of 20 are 1, 2, 4, 5, 10, 20
- Factors of 10 - The factors of 10 are 1, 2, 5, 10
- Factors of 36 - The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 234 by Prime Factorization
- 234 ÷ 2 = 117
Further dividing 117 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 117 by the next smallest prime factor. We stop ultimately if the next prime factor doesn't exist or when we can't divide any further.
So, the prime factorization of 234 can be written as 21 × 32 × 131 where 2, 3, 13 are prime.
Factors of 234 in Pairs
Pair factors of 234 are the pairs of numbers that when multiplied give the product 234. The factors of 234 in pairs are:
- 1 × 234 = (1, 234)
- 2 × 117 = (2, 117)
- 3 × 78 = (3, 78)
- 6 × 39 = (6, 39)
- 9 × 26 = (9, 26)
- 13 × 18 = (13, 18)
Negative pair factors of 234 are:
- -1 × -234 = (-1, -234)
- -2 × -117 = (-2, -117)
- -3 × -78 = (-3, -78)
- -6 × -39 = (-6, -39)
- -9 × -26 = (-9, -26)
- -13 × -18 = (-13, -18)
NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.
Factors of 234 Solved Examples
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Example 1: How many factors are there for 234?
Solution:
The factors of 234 are too many, therefore if we can find the prime factorization of 234, then the total number of factors can be calculated using the formula shown below.
If the prime factorization of the number is ax × by × cz where a, b, c are prime, then the total number of factors can be given by (x + 1)(y + 1)(z + 1).
Prime Factorization of 234 = 21 × 32 × 131
Therefore, the total number of factors are (1 + 1) × (2 + 1) × (1 + 1) = 2 × 3 × 2 = 12 -
Example 2: Find the LCM and Highest Common Factor (HCF) of 234 and 147.
Solution:
The factors of 234 are 1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117, 234 and factors of 147 are 1, 3, 7, 21, 49, 147.
Therefore, the LCM of 234 and 147 is 11466 and Highest Common Factor (HCF) of 234 and 147 is 3. -
Example 3: Find if 3, 9, 13, 18, 39, 78 and 230 are factors of 234.
Solution:
When we divide 234 by 230 it leaves a remainder. Therefore, the number 230 is not a factor of 234. All numbers except 230 are factors of 234.
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Example 4: Find the product of all the prime factors of 234.
Solution:
Since, the prime factors of 234 are 2, 3, 13. Therefore, the product of prime factors = 2 × 3 × 13 = 78.
FAQs on Factors of 234
What are the Factors of 234?
The factors of 234 are 1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117, 234 and its negative factors are -1, -2, -3, -6, -9, -13, -18, -26, -39, -78, -117, -234.
What is the Sum of the Factors of 234?
Sum of all factors of 234 = (21 + 1 - 1)/(2 - 1) × (32 + 1 - 1)/(3 - 1) × (131 + 1 - 1)/(13 - 1) = 546
What numbers are the Pair Factors of 234?
The pair factors of 234 are (1, 234), (2, 117), (3, 78), (6, 39), (9, 26), (13, 18).
What is the Greatest Common Factor of 234 and 171?
The factors of 234 and 171 are 1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117, 234 and 1, 3, 9, 19, 57, 171 respectively.
Common factors of 234 and 171 are [1, 3, 9].
Hence, the Greatest Common Factor (GCF) of 234 and 171 is 9.
How Many Factors of 234 are also Factors of 156?
Since, the factors of 234 are 1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117, 234 and the factors of 156 are 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156.
Hence, [1, 2, 3, 6, 13, 26, 39, 78] are the common factors of 234 and 156.
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