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Factors of 1323

Factors of 1323 are the list of integers that we can split evenly into 1323. There are overall 12 factors of 1323 among which 1323 is the biggest factor and 3, 7 are its prime factors. The Prime Factorization of 1323 is 33 × 72.

  • All Factors of 1323: 1, 3, 7, 9, 21, 27, 49, 63, 147, 189, 441 and 1323
  • Prime Factors of 1323: 3, 7
  • Prime Factorization of 1323: 33 × 72
  • Sum of Factors of 1323: 2280
1. What Are the Factors of 1323?
2. Factors of 1323 by Prime Factorization
3. Factors of 1323 in Pairs
4. FAQs on Factors of 1323
Factors of 1323

What are Factors of 1323?

Factors of 1323 are pairs of those numbers whose products result in 1323. These factors are either prime numbers or composite numbers.

How to Find the Factors of 1323?

To find the factors of 1323, we will have to find the list of numbers that would divide 1323 without leaving any remainder.

  • 1323/441 = 3; therefore, 441 is a factor of 1323 and 3 is also a factor of 1323.
  • 1323/27 = 49; therefore, 27 is a factor of 1323 and 49 is also a factor of 1323.
Similarly we can find other factors. Hence, the factors of 1323 are 1, 3, 7, 9, 21, 27, 49, 63, 147, 189, 441, 1323.

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Factors of 1323 by Prime Factorization

The number 1323 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 1323. The first step is to divide the number 1323 with the smallest prime factor, here it is 3. We keep dividing until it gives a non-zero remainder.
  • 1323 ÷ 3 = 441
  • 441 ÷ 3 = 147
  • 147 ÷ 3 = 49

Further dividing 49 by 3 gives a non-zero remainder. So we stop the process and continue dividing the number 49 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 1323 can be written as 33 × 72 where 3, 7 are prime.

 

Factors of 1323 in Pairs

Pair factors of 1323 are the pairs of numbers that when multiplied give the product 1323. The factors of 1323 in pairs are:

  • 1 × 1323 = (1, 1323)
  • 3 × 441 = (3, 441)
  • 7 × 189 = (7, 189)
  • 9 × 147 = (9, 147)
  • 21 × 63 = (21, 63)
  • 27 × 49 = (27, 49)

Negative pair factors of 1323 are:

  • -1 × -1323 = (-1, -1323)
  • -3 × -441 = (-3, -441)
  • -7 × -189 = (-7, -189)
  • -9 × -147 = (-9, -147)
  • -21 × -63 = (-21, -63)
  • -27 × -49 = (-27, -49)

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

Factors of 1323 Solved Examples

  1. Example 1: How many factors are there for 1323?

    Solution:

    The factors of 1323 are too many, therefore if we can find the prime factorization of 1323, 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 1323 = 33 × 72
    Therefore, the total number of factors are (3 + 1) × (2 + 1) = 4 × 3 = 12

  2. Example 2: Find the Least Common Multiple (LCM) and Greatest Common Divisor (GCD) of 1323 and 98.

    Solution:

    The factors of 1323 are 1, 3, 7, 9, 21, 27, 49, 63, 147, 189, 441, 1323 and factors of 98 are 1, 2, 7, 14, 49, 98.

    Therefore, the Least Common Multiple (LCM) of 1323 and 98 is 2646 and Greatest Common Divisor (GCD) of 1323 and 98 is 49.

  3. Example 3: Find if 1, 3, 7, 21, 63, 147 and 1069 are factors of 1323.

    Solution:

    When we divide 1323 by 1069 it leaves a remainder. Therefore, the number 1069 is not a factor of 1323. All numbers except 1069 are factors of 1323.

  4. Example 4: Find the product of all the prime factors of 1323.

    Solution:

    Since, the prime factors of 1323 are 3, 7. Therefore, the product of prime factors = 3 × 7 = 21.

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FAQs on Factors of 1323

What are the Factors of 1323?

The factors of 1323 are 1, 3, 7, 9, 21, 27, 49, 63, 147, 189, 441, 1323 and its negative factors are -1, -3, -7, -9, -21, -27, -49, -63, -147, -189, -441, -1323.

What is the Sum of Factors of 1323?

Sum of all factors of 1323 = (33 + 1 - 1)/(3 - 1) × (72 + 1 - 1)/(7 - 1) = 2280

What numbers are the Pair Factors of 1323?

The pair factors of 1323 are (1, 1323), (3, 441), (7, 189), (9, 147), (21, 63), (27, 49).

What is the Greatest Common Factor of 1323 and 661?

The factors of 1323 are 1, 3, 7, 9, 21, 27, 49, 63, 147, 189, 441, 1323 and the factors of 661 are 1, 661. 1323 and 661 have only one common factor which is 1. This implies that 1323 and 661 are co-prime.

Hence, the Greatest Common Factor (GCF) of 1323 and 661 is 1.

How Many Factors of 1323 are also Factors of 782?

Since, the factors of 1323 are 1, 3, 7, 9, 21, 27, 49, 63, 147, 189, 441, 1323 and factors of 782 are 1, 2, 17, 23, 34, 46, 391, 782. Hence, 1323 and 782 have only one common factor which is 1. Therefore, 1323 and 782 are co-prime.

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