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Factors of 9604

Factors of 9604 are the list of integers that we can split evenly into 9604. There are total 15 factors of 9604, of which 2, 7 are its prime factors. The sum of all factors of 9604 is 19607.

  • All Factors of 9604: 1, 2, 4, 7, 14, 28, 49, 98, 196, 343, 686, 1372, 2401, 4802 and 9604
  • Prime Factors of 9604: 2, 7
  • Prime Factorization of 9604: 22 × 74
  • Sum of Factors of 9604: 19607
1. What Are the Factors of 9604?
2. Factors of 9604 by Prime Factorization
3. Factors of 9604 in Pairs
4. FAQs on Factors of 9604
Factors of 9604

What are Factors of 9604?

Factors of 9604 are pairs of those numbers whose products result in 9604. These factors are either prime numbers or composite numbers.

How to Find the Factors of 9604?

To find the factors of 9604, we will have to find the list of numbers that would divide 9604 without leaving any remainder.

  • 9604/686 = 14; therefore, 686 is a factor of 9604 and 14 is also a factor of 9604.
  • 9604/49 = 196; therefore, 49 is a factor of 9604 and 196 is also a factor of 9604.
Similarly we can find other factors. Hence, the factors of 9604 are 1, 2, 4, 7, 14, 28, 49, 98, 196, 343, 686, 1372, 2401, 4802, 9604.

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Factors of 9604 by Prime Factorization

The number 9604 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 9604. The first step is to divide the number 9604 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.
  • 9604 ÷ 2 = 4802
  • 4802 ÷ 2 = 2401

Further dividing 2401 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 2401 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 9604 can be written as 22 × 74 where 2, 7 are prime.

 

Factors of 9604 in Pairs

Pair factors of 9604 are the pairs of numbers that when multiplied give the product 9604. The factors of 9604 in pairs are:

  • 1 × 9604 = (1, 9604)
  • 2 × 4802 = (2, 4802)
  • 4 × 2401 = (4, 2401)
  • 7 × 1372 = (7, 1372)
  • 14 × 686 = (14, 686)
  • 28 × 343 = (28, 343)
  • 49 × 196 = (49, 196)
  • 98 × 98 = (98, 98)

Negative pair factors of 9604 are:

  • -1 × -9604 = (-1, -9604)
  • -2 × -4802 = (-2, -4802)
  • -4 × -2401 = (-4, -2401)
  • -7 × -1372 = (-7, -1372)
  • -14 × -686 = (-14, -686)
  • -28 × -343 = (-28, -343)
  • -49 × -196 = (-49, -196)
  • -98 × -98 = (-98, -98)

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

Factors of 9604 Solved Examples

  1. Example 1: How many factors are there for 9604?

    Solution:

    The factors of 9604 are too many, therefore if we can find the prime factorization of 9604, 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 9604 = 22 × 74
    Therefore, the total number of factors are (2 + 1) × (4 + 1) = 3 × 5 = 15

  2. Example 2: Find the Least Common Multiple and Greatest Common Divisor (GCD) of 9604 and 7286.

    Solution:

    The factors of 9604 are 1, 2, 4, 7, 14, 28, 49, 98, 196, 343, 686, 1372, 2401, 4802, 9604 and factors of 7286 are 1, 2, 3643, 7286.

    Therefore, the Least Common Multiple of 9604 and 7286 is 34987372 and Greatest Common Divisor (GCD) of 9604 and 7286 is 2.

  3. Example 3: Find if 1, 7, 49, 196, 343, 1152, 2401 and 4802 are factors of 9604.

    Solution:

    When we divide 9604 by 1152 it leaves a remainder. Therefore, the number 1152 is not a factor of 9604. All numbers except 1152 are factors of 9604.

  4. Example 4: Find the product of all the prime factors of 9604.

    Solution:

    Since, the prime factors of 9604 are 2, 7. Therefore, the product of prime factors = 2 × 7 = 14.

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FAQs on Factors of 9604

What are the Factors of 9604?

The factors of 9604 are 1, 2, 4, 7, 14, 28, 49, 98, 196, 343, 686, 1372, 2401, 4802, 9604 and its negative factors are -1, -2, -4, -7, -14, -28, -49, -98, -196, -343, -686, -1372, -2401, -4802, -9604.

What is the Sum of Factors of 9604?

Sum of all factors of 9604 = (22 + 1 - 1)/(2 - 1) × (74 + 1 - 1)/(7 - 1) = 19607

What are the Pair Factors of 9604?

The pair factors of 9604 are (1, 9604), (2, 4802), (4, 2401), (7, 1372), (14, 686), (28, 343), (49, 196), (98, 98).

What is the Greatest Common Factor of 9604 and 3133?

The factors of 9604 are 1, 2, 4, 7, 14, 28, 49, 98, 196, 343, 686, 1372, 2401, 4802, 9604 and the factors of 3133 are 1, 13, 241, 3133. 9604 and 3133 have only one common factor which is 1. This implies that 9604 and 3133 are co-prime.

Hence, the Greatest Common Factor (GCF) of 9604 and 3133 is 1.

How Many Factors of 9604 are also common to the Factors of 8147?

Since, the factors of 9604 are 1, 2, 4, 7, 14, 28, 49, 98, 196, 343, 686, 1372, 2401, 4802, 9604 and factors of 8147 are 1, 8147. Hence, 9604 and 8147 have only one common factor which is 1. Therefore, 9604 and 8147 are co-prime.

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