Factors of 2600
Factors of 2600 are the list of integers that we can split evenly into 2600. There are overall 24 factors of 2600 among which 2600 is the biggest factor and 2, 5, 13 are its prime factors. The sum of all factors of 2600 is 6510.
 All Factors of 2600: 1, 2, 4, 5, 8, 10, 13, 20, 25, 26, 40, 50, 52, 65, 100, 104, 130, 200, 260, 325, 520, 650, 1300 and 2600
 Prime Factors of 2600: 2, 5, 13
 Prime Factorization of 2600: 2^{3} × 5^{2} × 13^{1}
 Sum of Factors of 2600: 6510
1.  What Are the Factors of 2600? 
2.  Factors of 2600 by Prime Factorization 
3.  Factors of 2600 in Pairs 
4.  FAQs on Factors of 2600 
What are Factors of 2600?
Factors of 2600 are pairs of those numbers whose products result in 2600. These factors are either prime numbers or composite numbers.
How to Find the Factors of 2600?
To find the factors of 2600, we will have to find the list of numbers that would divide 2600 without leaving any remainder.
 2600/5 = 520; therefore, 5 is a factor of 2600 and 520 is also a factor of 2600.
 2600/1300 = 2; therefore, 1300 is a factor of 2600 and 2 is also a factor of 2600.
☛ Also Check:
 Factors of 17  The factors of 17 are 1, 17
 Factors of 15  The factors of 15 are 1, 3, 5, 15
 Factors of 52  The factors of 52 are 1, 2, 4, 13, 26, 52
 Factors of 20  The factors of 20 are 1, 2, 4, 5, 10, 20
 Factors of 27  The factors of 27 are 1, 3, 9, 27
Factors of 2600 by Prime Factorization
 2600 ÷ 2 = 1300
 1300 ÷ 2 = 650
 650 ÷ 2 = 325
Further dividing 325 by 2 gives a nonzero remainder. So we stop the process and continue dividing the number 325 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 2600 can be written as 2^{3} × 5^{2} × 13^{1} where 2, 5, 13 are prime.
Factors of 2600 in Pairs
Pair factors of 2600 are the pairs of numbers that when multiplied give the product 2600. The factors of 2600 in pairs are:
 1 × 2600 = (1, 2600)
 2 × 1300 = (2, 1300)
 4 × 650 = (4, 650)
 5 × 520 = (5, 520)
 8 × 325 = (8, 325)
 10 × 260 = (10, 260)
 13 × 200 = (13, 200)
 20 × 130 = (20, 130)
 25 × 104 = (25, 104)
 26 × 100 = (26, 100)
 40 × 65 = (40, 65)
 50 × 52 = (50, 52)
Negative pair factors of 2600 are:
 1 × 2600 = (1, 2600)
 2 × 1300 = (2, 1300)
 4 × 650 = (4, 650)
 5 × 520 = (5, 520)
 8 × 325 = (8, 325)
 10 × 260 = (10, 260)
 13 × 200 = (13, 200)
 20 × 130 = (20, 130)
 25 × 104 = (25, 104)
 26 × 100 = (26, 100)
 40 × 65 = (40, 65)
 50 × 52 = (50, 52)
NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.
Factors of 2600 Solved Examples

Example 1: How many factors are there for 2600?
Solution:
The factors of 2600 are too many, therefore if we can find the prime factorization of 2600, then the total number of factors can be calculated using the formula shown below.
If the prime factorization of the number is a^{x} × b^{y} × c^{z} 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 2600 = 2^{3} × 5^{2} × 13^{1}
Therefore, the total number of factors are (3 + 1) × (2 + 1) × (1 + 1) = 4 × 3 × 2 = 24 
Example 2: Find the Least Common Multiple (LCM) and Greatest Common Factor (GCF) of 2600 and 504.
Solution:
The factors of 2600 are 1, 2, 4, 5, 8, 10, 13, 20, 25, 26, 40, 50, 52, 65, 100, 104, 130, 200, 260, 325, 520, 650, 1300, 2600 and factors of 504 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 168, 252, 504.
Therefore, the Least Common Multiple (LCM) of 2600 and 504 is 163800 and Greatest Common Factor (GCF) of 2600 and 504 is 8. 
Example 3: Find if 1, 40, 52, 65, 104, 130, 1468 and 2600 are factors of 2600.
Solution:
When we divide 2600 by 1468 it leaves a remainder. Therefore, the number 1468 is not a factor of 2600. All numbers except 1468 are factors of 2600.

Example 4: Find the product of all the prime factors of 2600.
Solution:
Since, the prime factors of 2600 are 2, 5, 13. Therefore, the product of prime factors = 2 × 5 × 13 = 130.
FAQs on Factors of 2600
What are the Factors of 2600?
The factors of 2600 are 1, 2, 4, 5, 8, 10, 13, 20, 25, 26, 40, 50, 52, 65, 100, 104, 130, 200, 260, 325, 520, 650, 1300, 2600 and its negative factors are 1, 2, 4, 5, 8, 10, 13, 20, 25, 26, 40, 50, 52, 65, 100, 104, 130, 200, 260, 325, 520, 650, 1300, 2600.
What is the Sum of all Factors of 2600?
Sum of all factors of 2600 = (2^{3 + 1}  1)/(2  1) × (5^{2 + 1}  1)/(5  1) × (13^{1 + 1}  1)/(13  1) = 6510
What are the Pair Factors of 2600?
The pair factors of 2600 are (1, 2600), (2, 1300), (4, 650), (5, 520), (8, 325), (10, 260), (13, 200), (20, 130), (25, 104), (26, 100), (40, 65), (50, 52).
What is the Greatest Common Factor of 2600 and 771?
The factors of 2600 are 1, 2, 4, 5, 8, 10, 13, 20, 25, 26, 40, 50, 52, 65, 100, 104, 130, 200, 260, 325, 520, 650, 1300, 2600 and the factors of 771 are 1, 3, 257, 771. 2600 and 771 have only one common factor which is 1. This implies that 2600 and 771 are coprime.
Hence, the Greatest Common Factor (GCF) of 2600 and 771 is 1.
How Many Factors of 2600 are also common to the Factors of 1709?
Since, the factors of 2600 are 1, 2, 4, 5, 8, 10, 13, 20, 25, 26, 40, 50, 52, 65, 100, 104, 130, 200, 260, 325, 520, 650, 1300, 2600 and factors of 1709 are 1, 1709. Hence, 2600 and 1709 have only one common factor which is 1. Therefore, 2600 and 1709 are coprime.
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