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Factors of 1287

Factors of 1287 are integers that can be divided evenly into 1287. It has total 12 factors of which 1287 is the biggest factor and the prime factors of 1287 are 3, 11, 13. The sum of all factors of 1287 is 2184.

  • All Factors of 1287: 1, 3, 9, 11, 13, 33, 39, 99, 117, 143, 429 and 1287
  • Prime Factors of 1287: 3, 11, 13
  • Prime Factorization of 1287: 32 × 111 × 131
  • Sum of Factors of 1287: 2184
1. What Are the Factors of 1287?
2. Factors of 1287 by Prime Factorization
3. Factors of 1287 in Pairs
4. FAQs on Factors of 1287
Factors of 1287

What are Factors of 1287?

Factors of 1287 are pairs of those numbers whose products result in 1287. These factors are either prime numbers or composite numbers.

How to Find the Factors of 1287?

To find the factors of 1287, we will have to find the list of numbers that would divide 1287 without leaving any remainder.

  • 1287/1 = 1287; therefore, 1 is a factor of 1287.
  • 1287/11 = 117; therefore, 11 is a factor of 1287.
Similarly we can find other factors. Hence, the factors of 1287 are 1, 3, 9, 11, 13, 33, 39, 99, 117, 143, 429, 1287.

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Factors of 1287 by Prime Factorization

The number 1287 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 1287. The first step is to divide the number 1287 with the smallest prime factor, here it is 3. We keep dividing until it gives a non-zero remainder.
  • 1287 ÷ 3 = 429
  • 429 ÷ 3 = 143

Further dividing 143 by 3 gives a non-zero remainder. So we stop the process and continue dividing the number 143 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 1287 can be written as 32 × 111 × 131 where 3, 11, 13 are prime.

 

Factors of 1287 in Pairs

Pair factors of 1287 are the pairs of numbers that when multiplied give the product 1287. The factors of 1287 in pairs are:

  • 1 × 1287 = (1, 1287)
  • 3 × 429 = (3, 429)
  • 9 × 143 = (9, 143)
  • 11 × 117 = (11, 117)
  • 13 × 99 = (13, 99)
  • 33 × 39 = (33, 39)

Negative pair factors of 1287 are:

  • -1 × -1287 = (-1, -1287)
  • -3 × -429 = (-3, -429)
  • -9 × -143 = (-9, -143)
  • -11 × -117 = (-11, -117)
  • -13 × -99 = (-13, -99)
  • -33 × -39 = (-33, -39)

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

Factors of 1287 Solved Examples

  1. Example 1: How many factors are there for 1287?

    Solution:

    The factors of 1287 are too many, therefore if we can find the prime factorization of 1287, 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 1287 = 32 × 111 × 131
    Therefore, the total number of factors are (2 + 1) × (1 + 1) × (1 + 1) = 3 × 2 × 2 = 12

  2. Example 2: Find the Least Common Multiple (LCM) and Greatest Common Divisor (GCD) of 1287 and 87.

    Solution:

    The factors of 1287 are 1, 3, 9, 11, 13, 33, 39, 99, 117, 143, 429, 1287 and factors of 87 are 1, 3, 29, 87.

    Therefore, the Least Common Multiple (LCM) of 1287 and 87 is 37323 and Greatest Common Divisor (GCD) of 1287 and 87 is 3.

  3. Example 3: Find if 11, 39, 117, 143, 429, 1255 and 1287 are factors of 1287.

    Solution:

    When we divide 1287 by 1255 it leaves a remainder. Therefore, the number 1255 is not a factor of 1287. All numbers except 1255 are factors of 1287.

  4. Example 4: Find the product of all the prime factors of 1287.

    Solution:

    Since, the prime factors of 1287 are 3, 11, 13. Therefore, the product of prime factors = 3 × 11 × 13 = 429.

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FAQs on Factors of 1287

What are the Factors of 1287?

The factors of 1287 are 1, 3, 9, 11, 13, 33, 39, 99, 117, 143, 429, 1287 and its negative factors are -1, -3, -9, -11, -13, -33, -39, -99, -117, -143, -429, -1287.

What is the Sum of Factors of 1287?

Sum of all factors of 1287 = (32 + 1 - 1)/(3 - 1) × (111 + 1 - 1)/(11 - 1) × (131 + 1 - 1)/(13 - 1) = 2184

What are the Pair Factors of 1287?

The pair factors of 1287 are (1, 1287), (3, 429), (9, 143), (11, 117), (13, 99), (33, 39).

What is the Greatest Common Factor of 1287 and 323?

The factors of 1287 are 1, 3, 9, 11, 13, 33, 39, 99, 117, 143, 429, 1287 and the factors of 323 are 1, 17, 19, 323. 1287 and 323 have only one common factor which is 1. This implies that 1287 and 323 are co-prime.

Hence, the Greatest Common Factor (GCF) of 1287 and 323 is 1.

How Many Factors of 1097 are also common to the Factors of 1287?

Since, the factors of 1287 are 1, 3, 9, 11, 13, 33, 39, 99, 117, 143, 429, 1287 and factors of 1097 are 1, 1097. Hence, 1287 and 1097 have only one common factor which is 1. Therefore, 1287 and 1097 are co-prime.

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