Factors of 260
Factors of 260 are the list of integers that we can split evenly into 260. There are overall 12 factors of 260 among which 260 is the biggest factor and its prime factors are 2, 5, 13. The Prime Factorization of 260 is 22 × 51 × 131.
- All Factors of 260: 1, 2, 4, 5, 10, 13, 20, 26, 52, 65, 130 and 260
- Prime Factors of 260: 2, 5, 13
- Prime Factorization of 260: 22 × 51 × 131
- Sum of Factors of 260: 588
1. | What Are the Factors of 260? |
2. | Factors of 260 by Prime Factorization |
3. | Factors of 260 in Pairs |
4. | FAQs on Factors of 260 |
What are Factors of 260?
Factors of 260 are pairs of those numbers whose products result in 260. These factors are either prime numbers or composite numbers.
How to Find the Factors of 260?
To find the factors of 260, we will have to find the list of numbers that would divide 260 without leaving any remainder.
- 260/5 = 52; therefore, 5 is a factor of 260 and 52 is also a factor of 260.
- 260/26 = 10; therefore, 26 is a factor of 260 and 10 is also a factor of 260.
☛ Also Check:
- Factors of 20 - The factors of 20 are 1, 2, 4, 5, 10, 20
- Factors of 90 - The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
- Factors of 51 - The factors of 51 are 1, 3, 17, 51
- Factors of 98 - The factors of 98 are 1, 2, 7, 14, 49, 98
- Factors of 36 - The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 260 by Prime Factorization
- 260 ÷ 2 = 130
- 130 ÷ 2 = 65
Further dividing 65 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 65 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 260 can be written as 22 × 51 × 131 where 2, 5, 13 are prime.
Factors of 260 in Pairs
Pair factors of 260 are the pairs of numbers that when multiplied give the product 260. The factors of 260 in pairs are:
- 1 × 260 = (1, 260)
- 2 × 130 = (2, 130)
- 4 × 65 = (4, 65)
- 5 × 52 = (5, 52)
- 10 × 26 = (10, 26)
- 13 × 20 = (13, 20)
Negative pair factors of 260 are:
- -1 × -260 = (-1, -260)
- -2 × -130 = (-2, -130)
- -4 × -65 = (-4, -65)
- -5 × -52 = (-5, -52)
- -10 × -26 = (-10, -26)
- -13 × -20 = (-13, -20)
NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.
Factors of 260 Solved Examples
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Example 1: How many factors are there for 260?
Solution:
The factors of 260 are too many, therefore if we can find the prime factorization of 260, 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 260 = 22 × 51 × 131
Therefore, the total number of factors are (2 + 1) × (1 + 1) × (1 + 1) = 3 × 2 × 2 = 12 -
Example 2: Find the Least Common Multiple (LCM) and Greatest Common Divisor (GCD) of 260 and 242.
Solution:
The factors of 260 are 1, 2, 4, 5, 10, 13, 20, 26, 52, 65, 130, 260 and factors of 242 are 1, 2, 11, 22, 121, 242.
Therefore, the Least Common Multiple (LCM) of 260 and 242 is 31460 and Greatest Common Divisor (GCD) of 260 and 242 is 2. -
Example 3: Find if 5, 13, 20, 26, 52, 226 and 260 are factors of 260.
Solution:
When we divide 260 by 226 it leaves a remainder. Therefore, the number 226 is not a factor of 260. All numbers except 226 are factors of 260.
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Example 4: Find the product of all the prime factors of 260.
Solution:
Since, the prime factors of 260 are 2, 5, 13. Therefore, the product of prime factors = 2 × 5 × 13 = 130.
FAQs on Factors of 260
What are the Factors of 260?
The factors of 260 are 1, 2, 4, 5, 10, 13, 20, 26, 52, 65, 130, 260 and its negative factors are -1, -2, -4, -5, -10, -13, -20, -26, -52, -65, -130, -260.
What is the Sum of all the Factors of 260?
Sum of all factors of 260 = (22 + 1 - 1)/(2 - 1) × (51 + 1 - 1)/(5 - 1) × (131 + 1 - 1)/(13 - 1) = 588
What are the Pair Factors of 260?
The pair factors of 260 are (1, 260), (2, 130), (4, 65), (5, 52), (10, 26), (13, 20).
What is the Greatest Common Factor of 260 and 125?
The factors of 260 and 125 are 1, 2, 4, 5, 10, 13, 20, 26, 52, 65, 130, 260 and 1, 5, 25, 125 respectively.
Common factors of 260 and 125 are [1, 5].
Hence, the GCF of 260 and 125 is 5.
How Many Factors of 260 are also common to the Factors of 62?
Since, the factors of 260 are 1, 2, 4, 5, 10, 13, 20, 26, 52, 65, 130, 260 and the factors of 62 are 1, 2, 31, 62.
Hence, [1, 2] are the common factors of 260 and 62.
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