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Factors of 693

Factors of 693 are the list of integers that we can split evenly into 693. There are 12 factors of 693, of which the following are its prime factors 3, 7, 11. The sum of all factors of 693 is 1248.

  • All Factors of 693: 1, 3, 7, 9, 11, 21, 33, 63, 77, 99, 231 and 693
  • Prime Factors of 693: 3, 7, 11
  • Prime Factorization of 693: 32 × 71 × 111
  • Sum of Factors of 693: 1248
1. What Are the Factors of 693?
2. Factors of 693 by Prime Factorization
3. Factors of 693 in Pairs
4. FAQs on Factors of 693
Factors of 693

What are Factors of 693?

Factors of 693 are pairs of those numbers whose products result in 693. These factors are either prime numbers or composite numbers.

How to Find the Factors of 693?

To find the factors of 693, we will have to find the list of numbers that would divide 693 without leaving any remainder.

  • 693/7 = 99; therefore, 7 is a factor of 693 and 99 is also a factor of 693.
  • 693/11 = 63; therefore, 11 is a factor of 693 and 63 is also a factor of 693.
Similarly we can find other factors. Hence, the factors of 693 are 1, 3, 7, 9, 11, 21, 33, 63, 77, 99, 231, 693.

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Factors of 693 by Prime Factorization

The number 693 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 693. The first step is to divide the number 693 with the smallest prime factor, here it is 3. We keep dividing until it gives a non-zero remainder.
  • 693 ÷ 3 = 231
  • 231 ÷ 3 = 77

Further dividing 77 by 3 gives a non-zero remainder. So we stop the process and continue dividing the number 77 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 693 can be written as 32 × 71 × 111 where 3, 7, 11 are prime.

 

Factors of 693 in Pairs

Pair factors of 693 are the pairs of numbers that when multiplied give the product 693. The factors of 693 in pairs are:

  • 1 × 693 = (1, 693)
  • 3 × 231 = (3, 231)
  • 7 × 99 = (7, 99)
  • 9 × 77 = (9, 77)
  • 11 × 63 = (11, 63)
  • 21 × 33 = (21, 33)

Negative pair factors of 693 are:

  • -1 × -693 = (-1, -693)
  • -3 × -231 = (-3, -231)
  • -7 × -99 = (-7, -99)
  • -9 × -77 = (-9, -77)
  • -11 × -63 = (-11, -63)
  • -21 × -33 = (-21, -33)

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

Factors of 693 Solved Examples

  1. Example 1: How many factors are there for 693?

    Solution:

    The factors of 693 are too many, therefore if we can find the prime factorization of 693, 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 693 = 32 × 71 × 111
    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 Highest Common Factor (HCF) of 693 and 313.

    Solution:

    The factors of 693 are 1, 3, 7, 9, 11, 21, 33, 63, 77, 99, 231, 693 and factors of 313 are 1, 313.

    Therefore, the Lowest Common Multiple (LCM) of 693 and 313 is 216909 and Highest Common Factor (HCF) of 693 and 313 is 1.

  3. Example 3: Find if 3, 11, 21, 33, 231, 324 and 693 are factors of 693.

    Solution:

    When we divide 693 by 324 it leaves a remainder. Therefore, the number 324 is not a factor of 693. All numbers except 324 are factors of 693.

  4. Example 4: Find the product of all the prime factors of 693.

    Solution:

    Since, the prime factors of 693 are 3, 7, 11. Therefore, the product of prime factors = 3 × 7 × 11 = 231.

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FAQs on Factors of 693

What are the Factors of 693?

The factors of 693 are 1, 3, 7, 9, 11, 21, 33, 63, 77, 99, 231, 693 and its negative factors are -1, -3, -7, -9, -11, -21, -33, -63, -77, -99, -231, -693.

What is the Sum of the Factors of 693?

Sum of all factors of 693 = (32 + 1 - 1)/(3 - 1) × (71 + 1 - 1)/(7 - 1) × (111 + 1 - 1)/(11 - 1) = 1248

What are the Prime Factors of 693?

The prime factors of 693 are 3, 7, 11.

What is the Greatest Common Factor of 693 and 100?

The factors of 693 are 1, 3, 7, 9, 11, 21, 33, 63, 77, 99, 231, 693 and the factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, 100. 693 and 100 have only one common factor which is 1. This implies that 693 and 100 are co-prime.

Hence, the Greatest Common Factor (GCF) of 693 and 100 is 1.

What are the Common Factors of 693 and 173?

Since, the factors of 693 are 1, 3, 7, 9, 11, 21, 33, 63, 77, 99, 231, 693 and factors of 173 are 1, 173. Hence, 693 and 173 have only one common factor which is 1. Therefore, 693 and 173 are co-prime.

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