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Factors of 9999

Factors of 9999 are integers that can be divided evenly into 9999. There are 12 factors of 9999 of which 9999 itself is the biggest factor and its prime factors are 3, 11, 101 The sum of all factors of 9999 is 15912.

  • All Factors of 9999: 1, 3, 9, 11, 33, 99, 101, 303, 909, 1111, 3333 and 9999
  • Prime Factors of 9999: 3, 11, 101
  • Prime Factorization of 9999: 32 × 111 × 1011
  • Sum of Factors of 9999: 15912
1. What Are the Factors of 9999?
2. Factors of 9999 by Prime Factorization
3. Factors of 9999 in Pairs
4. FAQs on Factors of 9999
Factors of 9999

What are Factors of 9999?

Factors of 9999 are pairs of those numbers whose products result in 9999. These factors are either prime numbers or composite numbers.

How to Find the Factors of 9999?

To find the factors of 9999, we will have to find the list of numbers that would divide 9999 without leaving any remainder.

  • 9999/1 = 9999; therefore, 1 is a factor of 9999.
  • 9999/99 = 101; therefore, 99 is a factor of 9999.
Similarly we can find other factors. Hence, the factors of 9999 are 1, 3, 9, 11, 33, 99, 101, 303, 909, 1111, 3333, 9999.

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Factors of 9999 by Prime Factorization

The number 9999 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 9999. The first step is to divide the number 9999 with the smallest prime factor, here it is 3. We keep dividing until it gives a non-zero remainder.
  • 9999 ÷ 3 = 3333
  • 3333 ÷ 3 = 1111

Further dividing 1111 by 3 gives a non-zero remainder. So we stop the process and continue dividing the number 1111 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 9999 can be written as 32 × 111 × 1011 where 3, 11, 101 are prime.

 

Factors of 9999 in Pairs

Pair factors of 9999 are the pairs of numbers that when multiplied give the product 9999. The factors of 9999 in pairs are:

  • 1 × 9999 = (1, 9999)
  • 3 × 3333 = (3, 3333)
  • 9 × 1111 = (9, 1111)
  • 11 × 909 = (11, 909)
  • 33 × 303 = (33, 303)
  • 99 × 101 = (99, 101)

Negative pair factors of 9999 are:

  • -1 × -9999 = (-1, -9999)
  • -3 × -3333 = (-3, -3333)
  • -9 × -1111 = (-9, -1111)
  • -11 × -909 = (-11, -909)
  • -33 × -303 = (-33, -303)
  • -99 × -101 = (-99, -101)

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

Factors of 9999 Solved Examples

  1. Example 1: How many factors are there for 9999?

    Solution:

    The factors of 9999 are too many, therefore if we can find the prime factorization of 9999, 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 9999 = 32 × 111 × 1011
    Therefore, the total number of factors are (2 + 1) × (1 + 1) × (1 + 1) = 3 × 2 × 2 = 12

  2. Example 2: Find the Lowest Common Multiple (LCM) and Greatest Common Factor (GCF) of 9999 and 6042.

    Solution:

    The factors of 9999 are 1, 3, 9, 11, 33, 99, 101, 303, 909, 1111, 3333, 9999 and factors of 6042 are 1, 2, 3, 6, 19, 38, 53, 57, 106, 114, 159, 318, 1007, 2014, 3021, 6042.

    Therefore, the Lowest Common Multiple (LCM) of 9999 and 6042 is 20137986 and Greatest Common Factor (GCF) of 9999 and 6042 is 3.

  3. Example 3: Find if 1, 3, 9, 11, 987, 1111 and 3333 are factors of 9999.

    Solution:

    When we divide 9999 by 987 it leaves a remainder. Therefore, the number 987 is not a factor of 9999. All numbers except 987 are factors of 9999.

  4. Example 4: Find the product of all the prime factors of 9999.

    Solution:

    Since, the prime factors of 9999 are 3, 11, 101. Therefore, the product of prime factors = 3 × 11 × 101 = 3333.

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FAQs on Factors of 9999

What are the Factors of 9999?

The factors of 9999 are 1, 3, 9, 11, 33, 99, 101, 303, 909, 1111, 3333, 9999 and its negative factors are -1, -3, -9, -11, -33, -99, -101, -303, -909, -1111, -3333, -9999.

What is the Sum of all Factors of 9999?

Sum of all factors of 9999 = (32 + 1 - 1)/(3 - 1) × (111 + 1 - 1)/(11 - 1) × (1011 + 1 - 1)/(101 - 1) = 15912

What are the Pair Factors of 9999?

The pair factors of 9999 are (1, 9999), (3, 3333), (9, 1111), (11, 909), (33, 303), (99, 101).

What is the Greatest Common Factor of 9999 and 9433?

The factors of 9999 are 1, 3, 9, 11, 33, 99, 101, 303, 909, 1111, 3333, 9999 and the factors of 9433 are 1, 9433. 9999 and 9433 have only one common factor which is 1. This implies that 9999 and 9433 are co-prime.

Hence, the Greatest Common Factor (GCF) of 9999 and 9433 is 1.

How Many Factors of 9999 are also Factors of 215?

Since, the factors of 9999 are 1, 3, 9, 11, 33, 99, 101, 303, 909, 1111, 3333, 9999 and factors of 215 are 1, 5, 43, 215. Hence, 9999 and 215 have only one common factor which is 1. Therefore, 9999 and 215 are co-prime.

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