1. Steps to find factors of 2600 using Division Method

Example: Find factors of 2600

  • Divide 2600 by 1: 2600 ÷ 1 : Remainder = 0
  • Divide 2600 by 2: 2600 ÷ 2 : Remainder = 0
  • Divide 2600 by 4: 2600 ÷ 4 : Remainder = 0
  • Divide 2600 by 5: 2600 ÷ 5 : Remainder = 0
  • Divide 2600 by 8: 2600 ÷ 8 : Remainder = 0
  • Divide 2600 by 10: 2600 ÷ 10 : Remainder = 0
  • Divide 2600 by 13: 2600 ÷ 13 : Remainder = 0
  • Divide 2600 by 20: 2600 ÷ 20 : Remainder = 0
  • Divide 2600 by 25: 2600 ÷ 25 : Remainder = 0
  • Divide 2600 by 26: 2600 ÷ 26 : Remainder = 0
  • Divide 2600 by 40: 2600 ÷ 40 : Remainder = 0
  • Divide 2600 by 50: 2600 ÷ 50 : Remainder = 0
  • Divide 2600 by 52: 2600 ÷ 52 : Remainder = 0
  • Divide 2600 by 65: 2600 ÷ 65 : Remainder = 0
  • Divide 2600 by 100: 2600 ÷ 100 : Remainder = 0
  • Divide 2600 by 104: 2600 ÷ 104 : Remainder = 0
  • Divide 2600 by 130: 2600 ÷ 130 : Remainder = 0
  • Divide 2600 by 200: 2600 ÷ 200 : Remainder = 0
  • Divide 2600 by 260: 2600 ÷ 260 : Remainder = 0
  • Divide 2600 by 325: 2600 ÷ 325 : Remainder = 0
  • Divide 2600 by 520: 2600 ÷ 520 : Remainder = 0
  • Divide 2600 by 650: 2600 ÷ 650 : Remainder = 0
  • Divide 2600 by 1300: 2600 ÷ 1300 : Remainder = 0
  • Divide 2600 by 2600: 2600 ÷ 2600 : Remainder = 0

Hence, 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, and 2600

2. Steps to find factors of 2600 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

Method 1: Division Method

To find the primefactors of 2600 using the division method, follow these steps:

  • Step 1. Start dividing 2600 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
  • Step 2. After finding the smallest prime factor of the number 2600, which is 2. Divide 2600 by 2 to obtain the quotient (1300).
    2600 ÷ 2 = 1300
  • Step 3. Repeat step 1 with the obtained quotient (1300).
    1300 ÷ 2 = 650
    650 ÷ 2 = 325
    325 ÷ 5 = 65
    65 ÷ 5 = 13
    13 ÷ 13 = 1

So, the prime factorization of 2600 is, 2600 = 2 x 2 x 2 x 5 x 5 x 13.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 2600 as shown below:

So, the prime factorization of 2600 is, 2600 = 2 x 2 x 2 x 5 x 5 x 13.

3. Find factors of 2600 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 2600 would be the two numbers which, when multiplied, give 2600 as the result.

The following table represents the calculation of factors of 2600 in pairs:

Factor Pair Pair Factorization
1 and 2600 1 x 2600 = 2600
2 and 1300 2 x 1300 = 2600
4 and 650 4 x 650 = 2600
5 and 520 5 x 520 = 2600
8 and 325 8 x 325 = 2600
10 and 260 10 x 260 = 2600
13 and 200 13 x 200 = 2600
20 and 130 20 x 130 = 2600
25 and 104 25 x 104 = 2600
26 and 100 26 x 100 = 2600
40 and 65 40 x 65 = 2600
50 and 52 50 x 52 = 2600

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 2600. They are called negative pair factors.

Hence, the negative pairs of 2600 would be ( -1 , -2600 ) , ( -2 , -1300 ) , ( -4 , -650 ) , ( -5 , -520 ) , ( -8 , -325 ) , ( -10 , -260 ) , ( -13 , -200 ) , ( -20 , -130 ) , ( -25 , -104 ) , ( -26 , -100 ) , ( -40 , -65 ) and ( -50 , -52 ) .

What are factors?

In mathematics, a factor is that number which divides into another number exactly, without leaving a remainder. A factor of a number can be positive or negative.

Properties of factors

  • Each number is a factor of itself. Eg. 2600 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 2600.
  • Every number is a factor of zero (0), since 2600 x 0 = 0.
  • Every number other than 1 has at least two factors, namely the number itself and 1.
  • Every factor of a number is an exact divisor of that number, example 1, 2, 4, 5, 8, 10, 13, 20, 25, 26, 40, 50, 52, 65, 100, 104, 130, 200, 260, 325, 520, 650, 1300, 2600 are exact divisors of 2600.
  • 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. Each factor divides 2600 without leaving a remainder.
  • Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 5, 8, 10, 13, 20, 25, 26, 40, 50, 52, 65, 100, 104, 130, 200, 260, 325, 520, 650, 1300, 2600 are all less than or equal to 2600.

Frequently Asked Questions

  • What is prime factorization of 2600?

    Prime factorization of 2600 is 2 x 2 x 2 x 5 x 5 x 13.

  • How do you find factors of a negative number? ( eg. -2600 )?

    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.

  • What are the prime 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.
    Prime factors of 2600 are 2, 2, 2, 5, 5, 13.

  • What are 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 prime factors of 2600?

    The greatest prime factor of 2600 is 13.

  • What are six multiples of 2600?

    First five multiples of 2600 are 5200, 7800, 10400, 13000, 15600, 18200.

  • What are factors of 2600?

    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.

  • Which is the smallest prime factor of 2600?

    Smallest prime factor of 2600 is 2.

  • Is 2600 a whole number?

    Yes 2600 is a whole number.

Examples of Factors

Kevin has been asked to write 23 factor(s) of 2600. Can you predict the answer?

23 factor(s) 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.

Sammy is puzzled while calculating the prime factors of 2600. Can you help him find them?

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.
Prime factors of 2600 are 2, 2, 2, 5, 5, 13

What is prime factorization of 2600?

Prime factorization of 2600 is 2 x 2 x 2 x 5 x 5 x 13 = 23 x 52 x 13.

Ariel has been assigned the task to find the product of all the prime factors of 2600. Can you help her?

Prime factors of 2600 are 2, 2, 2, 5, 5, 13.
Hence, the product of prime factors of 130.

Can you help Rubel to find out the product of the even factors of 2600?

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.
Even factors of 2600 are 2, 4, 8, 10, 20, 26, 40, 50, 52, 100, 104, 130, 200, 260, 520, 650, 1300, 2600.
Hence, product of even factors of 2600 is; 2 x 4 x 8 x 10 x 20 x 26 x 40 x 50 x 52 x 100 x 104 x 130 x 200 x 260 x 520 x 650 x 1300 x 2600 = 2.779905883635712e+33.

Joy wants to calculate mean of all the factors of 2600. Help him in finding the mean of 2600.

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.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 2600 is 1 + 2 + 4 + 5 + 8 + 10 + 13 + 20 + 25 + 26 + 40 + 50 + 52 + 65 + 100 + 104 + 130 + 200 + 260 + 325 + 520 + 650 + 1300 + 2600 = 6510.
Hence, the mean of factors of 2600 is 6510 ÷ 24 = 271.25.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 2600? Help her in writing all the factors.

Positive 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.
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.