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Factors of 728

Factors of 728 are integers that can be divided evenly into 728. It has total 16 factors of which 728 is the biggest factor and the prime factors of 728 are 2, 7, 13. The sum of all factors of 728 is 1680.

  • All Factors of 728: 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364 and 728
  • Prime Factors of 728: 2, 7, 13
  • Prime Factorization of 728: 23 × 71 × 131
  • Sum of Factors of 728: 1680
1. What Are the Factors of 728?
2. Factors of 728 by Prime Factorization
3. Factors of 728 in Pairs
4. FAQs on Factors of 728
Factors of 728

What are Factors of 728?

Factors of 728 are pairs of those numbers whose products result in 728. These factors are either prime numbers or composite numbers.

How to Find the Factors of 728?

To find the factors of 728, we will have to find the list of numbers that would divide 728 without leaving any remainder.

  • 728/52 = 14; therefore, 52 is a factor of 728 and 14 is also a factor of 728.
  • 728/28 = 26; therefore, 28 is a factor of 728 and 26 is also a factor of 728.
Similarly we can find other factors. Hence, the factors of 728 are 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, 728.

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Factors of 728 by Prime Factorization

The number 728 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 728. The first step is to divide the number 728 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.
  • 728 ÷ 2 = 364
  • 364 ÷ 2 = 182
  • 182 ÷ 2 = 91

Further dividing 91 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 91 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 728 can be written as 23 × 71 × 131 where 2, 7, 13 are prime.

 

Factors of 728 in Pairs

Pair factors of 728 are the pairs of numbers that when multiplied give the product 728. The factors of 728 in pairs are:

  • 1 × 728 = (1, 728)
  • 2 × 364 = (2, 364)
  • 4 × 182 = (4, 182)
  • 7 × 104 = (7, 104)
  • 8 × 91 = (8, 91)
  • 13 × 56 = (13, 56)
  • 14 × 52 = (14, 52)
  • 26 × 28 = (26, 28)

Negative pair factors of 728 are:

  • -1 × -728 = (-1, -728)
  • -2 × -364 = (-2, -364)
  • -4 × -182 = (-4, -182)
  • -7 × -104 = (-7, -104)
  • -8 × -91 = (-8, -91)
  • -13 × -56 = (-13, -56)
  • -14 × -52 = (-14, -52)
  • -26 × -28 = (-26, -28)

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

Factors of 728 Solved Examples

  1. Example 1: How many factors are there for 728?

    Solution:

    The factors of 728 are too many, therefore if we can find the prime factorization of 728, 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 728 = 23 × 71 × 131
    Therefore, the total number of factors are (3 + 1) × (1 + 1) × (1 + 1) = 4 × 2 × 2 = 16

  2. Example 2: Find the Lowest Common Multiple (LCM) and Highest Common Factor (HCF) of 728 and 174.

    Solution:

    The factors of 728 are 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, 728 and factors of 174 are 1, 2, 3, 6, 29, 58, 87, 174.

    Therefore, the Lowest Common Multiple (LCM) of 728 and 174 is 63336 and Highest Common Factor (HCF) of 728 and 174 is 2.

  3. Example 3: Find if 1, 4, 26, 52, 56, 104, 549 and 728 are factors of 728.

    Solution:

    When we divide 728 by 549 it leaves a remainder. Therefore, the number 549 is not a factor of 728. All numbers except 549 are factors of 728.

  4. Example 4: Find the product of all the prime factors of 728.

    Solution:

    Since, the prime factors of 728 are 2, 7, 13. Therefore, the product of prime factors = 2 × 7 × 13 = 182.

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FAQs on Factors of 728

What are the Factors of 728?

The factors of 728 are 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, 728 and its negative factors are -1, -2, -4, -7, -8, -13, -14, -26, -28, -52, -56, -91, -104, -182, -364, -728.

What is the Sum of all Factors of 728?

Sum of all factors of 728 = (23 + 1 - 1)/(2 - 1) × (71 + 1 - 1)/(7 - 1) × (131 + 1 - 1)/(13 - 1) = 1680

What are the Prime Factors of 728?

The prime factors of 728 are 2, 7, 13.

What is the Greatest Common Factor of 728 and 702?

The factors of 728 and 702 are 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, 728 and 1, 2, 3, 6, 9, 13, 18, 26, 27, 39, 54, 78, 117, 234, 351, 702 respectively.

Common factors of 728 and 702 are [1, 2, 13, 26].

Hence, the Greatest Common Factor of 728 and 702 is 26.

What are the Common Factors of 728 and 243?

Since, the factors of 728 are 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, 728 and factors of 243 are 1, 3, 9, 27, 81, 243. Hence, 728 and 243 have only one common factor which is 1. Therefore, 728 and 243 are co-prime.

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