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Factors of 9801

Factors of 9801 are the list of integers that can be evenly divided into 9801. There are 15 factors of 9801 of which 9801 itself is the biggest factor and its prime factors are 3, 11 The sum of all factors of 9801 is 16093.

  • All Factors of 9801: 1, 3, 9, 11, 27, 33, 81, 99, 121, 297, 363, 891, 1089, 3267 and 9801
  • Prime Factors of 9801: 3, 11
  • Prime Factorization of 9801: 34 × 112
  • Sum of Factors of 9801: 16093
1. What Are the Factors of 9801?
2. Factors of 9801 by Prime Factorization
3. Factors of 9801 in Pairs
4. FAQs on Factors of 9801
Factors of 9801

What are Factors of 9801?

Factors of 9801 are pairs of those numbers whose products result in 9801. These factors are either prime numbers or composite numbers.

How to Find the Factors of 9801?

To find the factors of 9801, we will have to find the list of numbers that would divide 9801 without leaving any remainder.

  • 9801/33 = 297; therefore, 33 is a factor of 9801 and 297 is also a factor of 9801.
  • 9801/1089 = 9; therefore, 1089 is a factor of 9801 and 9 is also a factor of 9801.
Similarly we can find other factors. Hence, the factors of 9801 are 1, 3, 9, 11, 27, 33, 81, 99, 121, 297, 363, 891, 1089, 3267, 9801.

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Factors of 9801 by Prime Factorization

The number 9801 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 9801. The first step is to divide the number 9801 with the smallest prime factor, here it is 3. We keep dividing until it gives a non-zero remainder.
  • 9801 ÷ 3 = 3267
  • 3267 ÷ 3 = 1089
  • 1089 ÷ 3 = 363
  • 363 ÷ 3 = 121

Further dividing 121 by 3 gives a non-zero remainder. So we stop the process and continue dividing the number 121 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 9801 can be written as 34 × 112 where 3, 11 are prime.

 

Factors of 9801 in Pairs

Pair factors of 9801 are the pairs of numbers that when multiplied give the product 9801. The factors of 9801 in pairs are:

  • 1 × 9801 = (1, 9801)
  • 3 × 3267 = (3, 3267)
  • 9 × 1089 = (9, 1089)
  • 11 × 891 = (11, 891)
  • 27 × 363 = (27, 363)
  • 33 × 297 = (33, 297)
  • 81 × 121 = (81, 121)
  • 99 × 99 = (99, 99)

Negative pair factors of 9801 are:

  • -1 × -9801 = (-1, -9801)
  • -3 × -3267 = (-3, -3267)
  • -9 × -1089 = (-9, -1089)
  • -11 × -891 = (-11, -891)
  • -27 × -363 = (-27, -363)
  • -33 × -297 = (-33, -297)
  • -81 × -121 = (-81, -121)
  • -99 × -99 = (-99, -99)

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

Factors of 9801 Solved Examples

  1. Example 1: How many factors are there for 9801?

    Solution:

    The factors of 9801 are too many, therefore if we can find the prime factorization of 9801, 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 9801 = 34 × 112
    Therefore, the total number of factors are (4 + 1) × (2 + 1) = 5 × 3 = 15

  2. Example 2: Find the Least Common Multiple and Greatest Common Factor (GCF) of 9801 and 8715.

    Solution:

    The factors of 9801 are 1, 3, 9, 11, 27, 33, 81, 99, 121, 297, 363, 891, 1089, 3267, 9801 and factors of 8715 are 1, 3, 5, 7, 15, 21, 35, 83, 105, 249, 415, 581, 1245, 1743, 2905, 8715.

    Therefore, the Least Common Multiple of 9801 and 8715 is 28471905 and Greatest Common Factor (GCF) of 9801 and 8715 is 3.

  3. Example 3: Find if 1, 3, 9, 11, 33, 81, 297 and 8943 are factors of 9801.

    Solution:

    When we divide 9801 by 8943 it leaves a remainder. Therefore, the number 8943 is not a factor of 9801. All numbers except 8943 are factors of 9801.

  4. Example 4: Find the product of all the prime factors of 9801.

    Solution:

    Since, the prime factors of 9801 are 3, 11. Therefore, the product of prime factors = 3 × 11 = 33.

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FAQs on Factors of 9801

What are the Factors of 9801?

The factors of 9801 are 1, 3, 9, 11, 27, 33, 81, 99, 121, 297, 363, 891, 1089, 3267, 9801 and its negative factors are -1, -3, -9, -11, -27, -33, -81, -99, -121, -297, -363, -891, -1089, -3267, -9801.

What is the Sum of all the Factors of 9801?

Sum of all factors of 9801 = (34 + 1 - 1)/(3 - 1) × (112 + 1 - 1)/(11 - 1) = 16093

What numbers are the Pair Factors of 9801?

The pair factors of 9801 are (1, 9801), (3, 3267), (9, 1089), (11, 891), (27, 363), (33, 297), (81, 121), (99, 99).

What is the Greatest Common Factor of 9801 and 8169?

The factors of 9801 and 8169 are 1, 3, 9, 11, 27, 33, 81, 99, 121, 297, 363, 891, 1089, 3267, 9801 and 1, 3, 7, 21, 389, 1167, 2723, 8169 respectively.

Common factors of 9801 and 8169 are [1, 3].

Hence, the GCF of 9801 and 8169 is 3.

How Many Factors of 2620 are also common to the Factors of 9801?

Since, the factors of 9801 are 1, 3, 9, 11, 27, 33, 81, 99, 121, 297, 363, 891, 1089, 3267, 9801 and factors of 2620 are 1, 2, 4, 5, 10, 20, 131, 262, 524, 655, 1310, 2620. Hence, 9801 and 2620 have only one common factor which is 1. Therefore, 9801 and 2620 are co-prime.

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