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Factors of 5005

Factors of 5005 are the list of integers that we can split evenly into 5005. There are overall 16 factors of 5005 among which 5005 is the biggest factor and 5, 7, 11, 13 are its prime factors. The sum of all factors of 5005 is 8064.

  • All Factors of 5005: 1, 5, 7, 11, 13, 35, 55, 65, 77, 91, 143, 385, 455, 715, 1001 and 5005
  • Prime Factors of 5005: 5, 7, 11, 13
  • Prime Factorization of 5005: 51 × 71 × 111 × 131
  • Sum of Factors of 5005: 8064
1. What Are the Factors of 5005?
2. Factors of 5005 by Prime Factorization
3. Factors of 5005 in Pairs
4. FAQs on Factors of 5005
Factors of 5005

What are Factors of 5005?

Factors of 5005 are pairs of those numbers whose products result in 5005. These factors are either prime numbers or composite numbers.

How to Find the Factors of 5005?

To find the factors of 5005, we will have to find the list of numbers that would divide 5005 without leaving any remainder.

  • 5005/715 = 7; therefore, 715 is a factor of 5005 and 7 is also a factor of 5005.
  • 5005/143 = 35; therefore, 143 is a factor of 5005 and 35 is also a factor of 5005.
Similarly we can find other factors. Hence, the factors of 5005 are 1, 5, 7, 11, 13, 35, 55, 65, 77, 91, 143, 385, 455, 715, 1001, 5005.

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Factors of 5005 by Prime Factorization

The number 5005 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 5005. The first step is to divide the number 5005 with the smallest prime factor, here it is 5. We keep dividing until it gives a non-zero remainder.
  • 5005 ÷ 5 = 1001

Further dividing 1001 by 5 gives a non-zero remainder. So we stop the process and continue dividing the number 1001 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 5005 can be written as 51 × 71 × 111 × 131 where 5, 7, 11, 13 are prime.

 

Factors of 5005 in Pairs

Pair factors of 5005 are the pairs of numbers that when multiplied give the product 5005. The factors of 5005 in pairs are:

  • 1 × 5005 = (1, 5005)
  • 5 × 1001 = (5, 1001)
  • 7 × 715 = (7, 715)
  • 11 × 455 = (11, 455)
  • 13 × 385 = (13, 385)
  • 35 × 143 = (35, 143)
  • 55 × 91 = (55, 91)
  • 65 × 77 = (65, 77)

Negative pair factors of 5005 are:

  • -1 × -5005 = (-1, -5005)
  • -5 × -1001 = (-5, -1001)
  • -7 × -715 = (-7, -715)
  • -11 × -455 = (-11, -455)
  • -13 × -385 = (-13, -385)
  • -35 × -143 = (-35, -143)
  • -55 × -91 = (-55, -91)
  • -65 × -77 = (-65, -77)

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

Factors of 5005 Solved Examples

  1. Example 1: How many factors are there for 5005?

    Solution:

    The factors of 5005 are too many, therefore if we can find the prime factorization of 5005, 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 5005 = 51 × 71 × 111 × 131
    Therefore, the total number of factors are (1 + 1) × (1 + 1) × (1 + 1) × (1 + 1) = 2 × 2 × 2 × 2 = 16

  2. Example 2: Find the Least Common Multiple (LCM) and Highest Common Factor (HCF) of 5005 and 1267.

    Solution:

    The factors of 5005 are 1, 5, 7, 11, 13, 35, 55, 65, 77, 91, 143, 385, 455, 715, 1001, 5005 and factors of 1267 are 1, 7, 181, 1267.

    Therefore, the Least Common Multiple (LCM) of 5005 and 1267 is 905905 and Highest Common Factor (HCF) of 5005 and 1267 is 7.

  3. Example 3: Find if 7, 11, 91, 143, 455, 715, 1001 and 4032 are factors of 5005.

    Solution:

    When we divide 5005 by 4032 it leaves a remainder. Therefore, the number 4032 is not a factor of 5005. All numbers except 4032 are factors of 5005.

  4. Example 4: Find the product of all the prime factors of 5005.

    Solution:

    Since, the prime factors of 5005 are 5, 7, 11, 13. Therefore, the product of prime factors = 5 × 7 × 11 × 13 = 5005.

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FAQs on Factors of 5005

What are the Factors of 5005?

The factors of 5005 are 1, 5, 7, 11, 13, 35, 55, 65, 77, 91, 143, 385, 455, 715, 1001, 5005 and its negative factors are -1, -5, -7, -11, -13, -35, -55, -65, -77, -91, -143, -385, -455, -715, -1001, -5005.

What is the Sum of Factors of 5005?

Sum of all factors of 5005 = (51 + 1 - 1)/(5 - 1) × (71 + 1 - 1)/(7 - 1) × (111 + 1 - 1)/(11 - 1) × (131 + 1 - 1)/(13 - 1) = 8064

What Numbers are the Prime Factors of 5005?

The prime factors of 5005 are 5, 7, 11, 13.

What is the Greatest Common Factor of 5005 and 731?

The factors of 5005 are 1, 5, 7, 11, 13, 35, 55, 65, 77, 91, 143, 385, 455, 715, 1001, 5005 and the factors of 731 are 1, 17, 43, 731. 5005 and 731 have only one common factor which is 1. This implies that 5005 and 731 are co-prime.

Hence, the Greatest Common Factor (GCF) of 5005 and 731 is 1.

How Many Factors of 5005 are also common to the Factors of 3798?

Since, the factors of 5005 are 1, 5, 7, 11, 13, 35, 55, 65, 77, 91, 143, 385, 455, 715, 1001, 5005 and factors of 3798 are 1, 2, 3, 6, 9, 18, 211, 422, 633, 1266, 1899, 3798. Hence, 5005 and 3798 have only one common factor which is 1. Therefore, 5005 and 3798 are co-prime.

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