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Factors of 650

Factors of 650 are the list of integers that can be evenly divided into 650. There are overall 12 factors of 650 among which 650 is the biggest factor and 2, 5, 13 are its prime factors. The sum of all factors of 650 is 1302.

  • All Factors of 650: 1, 2, 5, 10, 13, 25, 26, 50, 65, 130, 325 and 650
  • Prime Factors of 650: 2, 5, 13
  • Prime Factorization of 650: 21 × 52 × 131
  • Sum of Factors of 650: 1302
1. What Are the Factors of 650?
2. Factors of 650 by Prime Factorization
3. Factors of 650 in Pairs
4. FAQs on Factors of 650
Factors of 650

What are Factors of 650?

Factors of 650 are pairs of those numbers whose products result in 650. These factors are either prime numbers or composite numbers.

How to Find the Factors of 650?

To find the factors of 650, we will have to find the list of numbers that would divide 650 without leaving any remainder.

  • 650/10 = 65; therefore, 10 is a factor of 650 and 65 is also a factor of 650.
  • 650/5 = 130; therefore, 5 is a factor of 650 and 130 is also a factor of 650.
Similarly we can find other factors. Hence, the factors of 650 are 1, 2, 5, 10, 13, 25, 26, 50, 65, 130, 325, 650.

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Factors of 650 by Prime Factorization

The number 650 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 650. The first step is to divide the number 650 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.
  • 650 ÷ 2 = 325

Further dividing 325 by 2 gives a non-zero 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 650 can be written as 21 × 52 × 131 where 2, 5, 13 are prime.

 

Factors of 650 in Pairs

Pair factors of 650 are the pairs of numbers that when multiplied give the product 650. The factors of 650 in pairs are:

  • 1 × 650 = (1, 650)
  • 2 × 325 = (2, 325)
  • 5 × 130 = (5, 130)
  • 10 × 65 = (10, 65)
  • 13 × 50 = (13, 50)
  • 25 × 26 = (25, 26)

Negative pair factors of 650 are:

  • -1 × -650 = (-1, -650)
  • -2 × -325 = (-2, -325)
  • -5 × -130 = (-5, -130)
  • -10 × -65 = (-10, -65)
  • -13 × -50 = (-13, -50)
  • -25 × -26 = (-25, -26)

NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.

Factors of 650 Solved Examples

  1. Example 1: How many factors are there for 650?

    Solution:

    The factors of 650 are too many, therefore if we can find the prime factorization of 650, 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 650 = 21 × 52 × 131
    Therefore, the total number of factors are (1 + 1) × (2 + 1) × (1 + 1) = 2 × 3 × 2 = 12

  2. Example 2: Find the Least Common Multiple and Greatest Common Factor (GCF) of 650 and 82.

    Solution:

    The factors of 650 are 1, 2, 5, 10, 13, 25, 26, 50, 65, 130, 325, 650 and factors of 82 are 1, 2, 41, 82.

    Therefore, the Least Common Multiple of 650 and 82 is 26650 and Greatest Common Factor (GCF) of 650 and 82 is 2.

  3. Example 3: Find if 1, 5, 65, 130, 325, 393 and 650 are factors of 650.

    Solution:

    When we divide 650 by 393 it leaves a remainder. Therefore, the number 393 is not a factor of 650. All numbers except 393 are factors of 650.

  4. Example 4: Find the product of all the prime factors of 650.

    Solution:

    Since, the prime factors of 650 are 2, 5, 13. Therefore, the product of prime factors = 2 × 5 × 13 = 130.

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FAQs on Factors of 650

What are the Factors of 650?

The factors of 650 are 1, 2, 5, 10, 13, 25, 26, 50, 65, 130, 325, 650 and its negative factors are -1, -2, -5, -10, -13, -25, -26, -50, -65, -130, -325, -650.

What is the Sum of the Factors of 650?

Sum of all factors of 650 = (21 + 1 - 1)/(2 - 1) × (52 + 1 - 1)/(5 - 1) × (131 + 1 - 1)/(13 - 1) = 1302

What are the Pair Factors of 650?

The pair factors of 650 are (1, 650), (2, 325), (5, 130), (10, 65), (13, 50), (25, 26).

What is the Greatest Common Factor of 650 and 396?

The factors of 650 and 396 are 1, 2, 5, 10, 13, 25, 26, 50, 65, 130, 325, 650 and 1, 2, 3, 4, 6, 9, 11, 12, 18, 22, 33, 36, 44, 66, 99, 132, 198, 396 respectively.

Common factors of 650 and 396 are [1, 2].

Hence, the Greatest Common Factor of 650 and 396 is 2.

What are the Common Factors of 650 and 511?

Since, the factors of 650 are 1, 2, 5, 10, 13, 25, 26, 50, 65, 130, 325, 650 and factors of 511 are 1, 7, 73, 511. Hence, 650 and 511 have only one common factor which is 1. Therefore, 650 and 511 are co-prime.

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