Factors of 264
Factors of 264 are the list of integers that we can split evenly into 264. There are 16 factors of 264 of which 264 itself is the biggest factor and its prime factors are 2, 3, 11 The Prime Factorization of 264 is 23 × 31 × 111.
- All Factors of 264: 1, 2, 3, 4, 6, 8, 11, 12, 22, 24, 33, 44, 66, 88, 132 and 264
- Prime Factors of 264: 2, 3, 11
- Prime Factorization of 264: 23 × 31 × 111
- Sum of Factors of 264: 720
1. | What Are the Factors of 264? |
2. | Factors of 264 by Prime Factorization |
3. | Factors of 264 in Pairs |
4. | FAQs on Factors of 264 |
What are Factors of 264?
Factors of 264 are pairs of those numbers whose products result in 264. These factors are either prime numbers or composite numbers.
How to Find the Factors of 264?
To find the factors of 264, we will have to find the list of numbers that would divide 264 without leaving any remainder.
- 264/22 = 12; therefore, 22 is a factor of 264 and 12 is also a factor of 264.
- 264/8 = 33; therefore, 8 is a factor of 264 and 33 is also a factor of 264.
☛ Also Check:
- Factors of 81 - The factors of 81 are 1, 3, 9, 27, 81
- Factors of 49 - The factors of 49 are 1, 7, 49
- Factors of 63 - The factors of 63 are 1, 3, 7, 9, 21, 63
- Factors of 5 - The factors of 5 are 1, 5
- Factors of 28 - The factors of 28 are 1, 2, 4, 7, 14, 28
Factors of 264 by Prime Factorization
- 264 ÷ 2 = 132
- 132 ÷ 2 = 66
- 66 ÷ 2 = 33
Further dividing 33 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 33 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 264 can be written as 23 × 31 × 111 where 2, 3, 11 are prime.
Factors of 264 in Pairs
Pair factors of 264 are the pairs of numbers that when multiplied give the product 264. The factors of 264 in pairs are:
- 1 × 264 = (1, 264)
- 2 × 132 = (2, 132)
- 3 × 88 = (3, 88)
- 4 × 66 = (4, 66)
- 6 × 44 = (6, 44)
- 8 × 33 = (8, 33)
- 11 × 24 = (11, 24)
- 12 × 22 = (12, 22)
Negative pair factors of 264 are:
- -1 × -264 = (-1, -264)
- -2 × -132 = (-2, -132)
- -3 × -88 = (-3, -88)
- -4 × -66 = (-4, -66)
- -6 × -44 = (-6, -44)
- -8 × -33 = (-8, -33)
- -11 × -24 = (-11, -24)
- -12 × -22 = (-12, -22)
NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.
Factors of 264 Solved Examples
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Example 1: How many factors are there for 264?
Solution:
The factors of 264 are too many, therefore if we can find the prime factorization of 264, 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 264 = 23 × 31 × 111
Therefore, the total number of factors are (3 + 1) × (1 + 1) × (1 + 1) = 4 × 2 × 2 = 16 -
Example 2: Find the LCM and Highest Common Factor (HCF) of 264 and 130.
Solution:
The factors of 264 are 1, 2, 3, 4, 6, 8, 11, 12, 22, 24, 33, 44, 66, 88, 132, 264 and factors of 130 are 1, 2, 5, 10, 13, 26, 65, 130.
Therefore, the LCM of 264 and 130 is 17160 and Highest Common Factor (HCF) of 264 and 130 is 2. -
Example 3: Find if 1, 3, 4, 6, 8, 11, 12 and 132 are factors of 264.
Solution:
When we divide 264 by 1, 3, 4, 6, 8, 11, 12, 132 it doesn't leave any remainder. Therefore, 1, 3, 4, 6, 8, 11, 12, 132 are factors of 264.
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Example 4: Find the product of all the prime factors of 264.
Solution:
Since, the prime factors of 264 are 2, 3, 11. Therefore, the product of prime factors = 2 × 3 × 11 = 66.
FAQs on Factors of 264
What are the Factors of 264?
The factors of 264 are 1, 2, 3, 4, 6, 8, 11, 12, 22, 24, 33, 44, 66, 88, 132, 264 and its negative factors are -1, -2, -3, -4, -6, -8, -11, -12, -22, -24, -33, -44, -66, -88, -132, -264.
What is the Sum of the Factors of 264?
Sum of all factors of 264 = (23 + 1 - 1)/(2 - 1) × (31 + 1 - 1)/(3 - 1) × (111 + 1 - 1)/(11 - 1) = 720
What Numbers are the Prime Factors of 264?
The prime factors of 264 are 2, 3, 11.
What is the Greatest Common Factor of 264 and 202?
The factors of 264 and 202 are 1, 2, 3, 4, 6, 8, 11, 12, 22, 24, 33, 44, 66, 88, 132, 264 and 1, 2, 101, 202 respectively.
Common factors of 264 and 202 are [1, 2].
Hence, the Greatest Common Factor (GCF) of 264 and 202 is 2.
How Many Factors of 264 are also Factors of 95?
Since, the factors of 264 are 1, 2, 3, 4, 6, 8, 11, 12, 22, 24, 33, 44, 66, 88, 132, 264 and factors of 95 are 1, 5, 19, 95. Hence, 264 and 95 have only one common factor which is 1. Therefore, 264 and 95 are co-prime.
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