Factors of 268
Factors of 268 are integers that can be divided evenly into 268. There are overall 6 factors of 268 among which 268 is the biggest factor and 1, 2, 4, 67, 134, 268 are positive factors. The Prime Factors and Pair Factors of 268 are 2 × 67 and (1, 268), (2, 134), (4, 67) respectively.
- All Factors of 268: 1, 2, 4, 67, 134 and 268
- Negative Factors of 268: -1, -2, -4, -67, -134 and -268
- Prime Factors of 268: 2, 67
- Prime Factorization of 268: 22 × 671
- Sum of Factors of 268: 476
1. | What Are the Factors of 268? |
2. | Factors of 268 by Prime Factorization |
3. | Factors of 268 in Pairs |
4. | FAQs on Factors of 268 |
What are Factors of 268?
Factors of 268 are pairs of those numbers whose products result in 268. These factors are either prime numbers or composite numbers.
How to Find the Factors of 268?
To find the factors of 268, we will have to find the list of numbers that would divide 268 without leaving any remainder.
- 268/67 = 4; therefore, 67 is a factor of 268 and 4 is also a factor of 268.
- 268/134 = 2; therefore, 134 is a factor of 268 and 2 is also a factor of 268.
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Factors of 268 by Prime Factorization
- 268 ÷ 2 = 134
- 134 ÷ 2 = 67
Further dividing 67 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 67 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 268 can be written as 22 × 671 where 2, 67 are prime.
Factors of 268 in Pairs
Pair factors of 268 are the pairs of numbers that when multiplied give the product 268. The factors of 268 in pairs are:
- 1 × 268 = (1, 268)
- 2 × 134 = (2, 134)
- 4 × 67 = (4, 67)
Negative pair factors of 268 are:
- -1 × -268 = (-1, -268)
- -2 × -134 = (-2, -134)
- -4 × -67 = (-4, -67)
NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.
Factors of 268 Solved Examples
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Example 1: How many factors are there for 268?
Solution:
The factors of 268 are 1, 2, 4, 67, 134, 268. Therefore, 268 has 6 factors.
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Example 2: Find the Least Common Multiple and Highest Common Factor (HCF) of 268 and 66.
Solution:
The factors of 268 are 1, 2, 4, 67, 134, 268 and factors of 66 are 1, 2, 3, 6, 11, 22, 33, 66.
Therefore, the Least Common Multiple of 268 and 66 is 8844 and Highest Common Factor (HCF) of 268 and 66 is 2. -
Example 3: Find if 1, 2, 67 and 165 are factors of 268.
Solution:
When we divide 268 by 165 it leaves a remainder. Therefore, the number 165 is not a factor of 268. All numbers except 165 are factors of 268.
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Example 4: Find the product of all the prime factors of 268.
Solution:
Since, the prime factors of 268 are 2, 67. Therefore, the product of prime factors = 2 × 67 = 134.
FAQs on Factors of 268
What are the Factors of 268?
The factors of 268 are 1, 2, 4, 67, 134, 268 and its negative factors are -1, -2, -4, -67, -134, -268.
What is the Sum of the Factors of 268?
Since, all factors of 268 are 1, 2, 4, 67, 134, 268 therefore, the sum of its factors is 1 + 2 + 4 + 67 + 134 + 268 = 476.
What are Pair Factors of 268?
The pair factors of 268 are (1, 268), (2, 134), (4, 67).
What is the Greatest Common Factor of 268 and 258?
The factors of 268 and 258 are 1, 2, 4, 67, 134, 268 and 1, 2, 3, 6, 43, 86, 129, 258 respectively.
Common factors of 268 and 258 are [1, 2].
Hence, the GCF of 268 and 258 is 2.
How Many Factors of 193 are also common to the Factors of 268?
Since, the factors of 268 are 1, 2, 4, 67, 134, 268 and factors of 193 are 1, 193. Hence, 268 and 193 have only one common factor which is 1. Therefore, 268 and 193 are co-prime.
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