Factors of 468
Factors of 468 are numbers that, when multiplied in pairs give the product as 468. There are overall 18 factors of 468 among which 468 is the biggest factor and its prime factors are 2, 3, 13. The sum of all factors of 468 is 1274.
- All Factors of 468: 1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 36, 39, 52, 78, 117, 156, 234 and 468
- Prime Factors of 468: 2, 3, 13
- Prime Factorization of 468: 22 × 32 × 131
- Sum of Factors of 468: 1274
1. | What Are the Factors of 468? |
2. | Factors of 468 by Prime Factorization |
3. | Factors of 468 in Pairs |
4. | FAQs on Factors of 468 |
What are Factors of 468?
Factors of 468 are pairs of those numbers whose products result in 468. These factors are either prime numbers or composite numbers.
How to Find the Factors of 468?
To find the factors of 468, we will have to find the list of numbers that would divide 468 without leaving any remainder.
- 468/9 = 52; therefore, 9 is a factor of 468 and 52 is also a factor of 468.
- 468/12 = 39; therefore, 12 is a factor of 468 and 39 is also a factor of 468.
☛ Also Check:
- Factors of 128 - The factors of 128 are 1, 2, 4, 8, 16, 32, 64, 128
- Factors of 54 - The factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54
- Factors of 75 - The factors of 75 are 1, 3, 5, 15, 25, 75
- Factors of 30 - The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30
- Factors of 121 - The factors of 121 are 1, 11, 121
Factors of 468 by Prime Factorization
- 468 ÷ 2 = 234
- 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 468 can be written as 22 × 32 × 131 where 2, 3, 13 are prime.
Factors of 468 in Pairs
Pair factors of 468 are the pairs of numbers that when multiplied give the product 468. The factors of 468 in pairs are:
- 1 × 468 = (1, 468)
- 2 × 234 = (2, 234)
- 3 × 156 = (3, 156)
- 4 × 117 = (4, 117)
- 6 × 78 = (6, 78)
- 9 × 52 = (9, 52)
- 12 × 39 = (12, 39)
- 13 × 36 = (13, 36)
- 18 × 26 = (18, 26)
Negative pair factors of 468 are:
- -1 × -468 = (-1, -468)
- -2 × -234 = (-2, -234)
- -3 × -156 = (-3, -156)
- -4 × -117 = (-4, -117)
- -6 × -78 = (-6, -78)
- -9 × -52 = (-9, -52)
- -12 × -39 = (-12, -39)
- -13 × -36 = (-13, -36)
- -18 × -26 = (-18, -26)
NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.
Factors of 468 Solved Examples
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Example 1: How many factors are there for 468?
Solution:
The factors of 468 are too many, therefore if we can find the prime factorization of 468, 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 468 = 22 × 32 × 131
Therefore, the total number of factors are (2 + 1) × (2 + 1) × (1 + 1) = 3 × 3 × 2 = 18 -
Example 2: Find the Least Common Multiple and Greatest Common Divisor (GCD) of 468 and 205.
Solution:
The factors of 468 are 1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 36, 39, 52, 78, 117, 156, 234, 468 and factors of 205 are 1, 5, 41, 205.
Therefore, the Least Common Multiple of 468 and 205 is 95940 and Greatest Common Divisor (GCD) of 468 and 205 is 1. -
Example 3: Find if 1, 12, 18, 26, 36, 52, 234 and 413 are factors of 468.
Solution:
When we divide 468 by 413 it leaves a remainder. Therefore, the number 413 is not a factor of 468. All numbers except 413 are factors of 468.
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Example 4: Find the product of all the prime factors of 468.
Solution:
Since, the prime factors of 468 are 2, 3, 13. Therefore, the product of prime factors = 2 × 3 × 13 = 78.
FAQs on Factors of 468
What are the Factors of 468?
The factors of 468 are 1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 36, 39, 52, 78, 117, 156, 234, 468 and its negative factors are -1, -2, -3, -4, -6, -9, -12, -13, -18, -26, -36, -39, -52, -78, -117, -156, -234, -468.
What is the Sum of all the Factors of 468?
Sum of all factors of 468 = (22 + 1 - 1)/(2 - 1) × (32 + 1 - 1)/(3 - 1) × (131 + 1 - 1)/(13 - 1) = 1274
What are Prime Factors of 468?
The prime factors of 468 are 2, 3, 13.
What is the Greatest Common Factor of 468 and 94?
The factors of 468 and 94 are 1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 36, 39, 52, 78, 117, 156, 234, 468 and 1, 2, 47, 94 respectively.
Common factors of 468 and 94 are [1, 2].
Hence, the Greatest Common Factor (GCF) of 468 and 94 is 2.
How Many Factors of 468 are also common to the Factors of 266?
Since, the factors of 468 are 1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 36, 39, 52, 78, 117, 156, 234, 468 and the factors of 266 are 1, 2, 7, 14, 19, 38, 133, 266.
Hence, [1, 2] are the common factors of 468 and 266.
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