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Factors of 1071

Factors of 1071 are numbers that, when multiplied in pairs give the product as 1071. It has total 12 factors of which 1071 is the biggest factor and the prime factors of 1071 are 3, 7, 17. The Prime Factorization of 1071 is 32 × 71 × 171.

  • All Factors of 1071: 1, 3, 7, 9, 17, 21, 51, 63, 119, 153, 357 and 1071
  • Prime Factors of 1071: 3, 7, 17
  • Prime Factorization of 1071: 32 × 71 × 171
  • Sum of Factors of 1071: 1872
1. What Are the Factors of 1071?
2. Factors of 1071 by Prime Factorization
3. Factors of 1071 in Pairs
4. FAQs on Factors of 1071
Factors of 1071

What are Factors of 1071?

Factors of 1071 are pairs of those numbers whose products result in 1071. These factors are either prime numbers or composite numbers.

How to Find the Factors of 1071?

To find the factors of 1071, we will have to find the list of numbers that would divide 1071 without leaving any remainder.

  • 1071/3 = 357; therefore, 3 is a factor of 1071 and 357 is also a factor of 1071.
  • 1071/51 = 21; therefore, 51 is a factor of 1071 and 21 is also a factor of 1071.
Similarly we can find other factors. Hence, the factors of 1071 are 1, 3, 7, 9, 17, 21, 51, 63, 119, 153, 357, 1071.

☛ Also Check:

  • Factors of 70 - The factors of 70 are 1, 2, 5, 7, 10, 14, 35, 70
  • Factors of 90 - The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
  • Factors of 28 - The factors of 28 are 1, 2, 4, 7, 14, 28
  • Factors of 108 - The factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
  • Factors of 96 - The factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96

Factors of 1071 by Prime Factorization

The number 1071 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 1071. The first step is to divide the number 1071 with the smallest prime factor, here it is 3. We keep dividing until it gives a non-zero remainder.
  • 1071 ÷ 3 = 357
  • 357 ÷ 3 = 119

Further dividing 119 by 3 gives a non-zero remainder. So we stop the process and continue dividing the number 119 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 1071 can be written as 32 × 71 × 171 where 3, 7, 17 are prime.

 

Factors of 1071 in Pairs

Pair factors of 1071 are the pairs of numbers that when multiplied give the product 1071. The factors of 1071 in pairs are:

  • 1 × 1071 = (1, 1071)
  • 3 × 357 = (3, 357)
  • 7 × 153 = (7, 153)
  • 9 × 119 = (9, 119)
  • 17 × 63 = (17, 63)
  • 21 × 51 = (21, 51)

Negative pair factors of 1071 are:

  • -1 × -1071 = (-1, -1071)
  • -3 × -357 = (-3, -357)
  • -7 × -153 = (-7, -153)
  • -9 × -119 = (-9, -119)
  • -17 × -63 = (-17, -63)
  • -21 × -51 = (-21, -51)

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

Factors of 1071 Solved Examples

  1. Example 1: How many factors are there for 1071?

    Solution:

    The factors of 1071 are too many, therefore if we can find the prime factorization of 1071, 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 1071 = 32 × 71 × 171
    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 Factor (GCF) of 1071 and 501.

    Solution:

    The factors of 1071 are 1, 3, 7, 9, 17, 21, 51, 63, 119, 153, 357, 1071 and factors of 501 are 1, 3, 167, 501.

    Therefore, the Least Common Multiple (LCM) of 1071 and 501 is 178857 and Greatest Common Factor (GCF) of 1071 and 501 is 3.

  3. Example 3: Find if 17, 21, 51, 63, 153, 357 and 369 are factors of 1071.

    Solution:

    When we divide 1071 by 369 it leaves a remainder. Therefore, the number 369 is not a factor of 1071. All numbers except 369 are factors of 1071.

  4. Example 4: Find the product of all the prime factors of 1071.

    Solution:

    Since, the prime factors of 1071 are 3, 7, 17. Therefore, the product of prime factors = 3 × 7 × 17 = 357.

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FAQs on Factors of 1071

What are the Factors of 1071?

The factors of 1071 are 1, 3, 7, 9, 17, 21, 51, 63, 119, 153, 357, 1071 and its negative factors are -1, -3, -7, -9, -17, -21, -51, -63, -119, -153, -357, -1071.

What is the Sum of all the Factors of 1071?

Sum of all factors of 1071 = (32 + 1 - 1)/(3 - 1) × (71 + 1 - 1)/(7 - 1) × (171 + 1 - 1)/(17 - 1) = 1872

What are the Pair Factors of 1071?

The pair factors of 1071 are (1, 1071), (3, 357), (7, 153), (9, 119), (17, 63), (21, 51).

What is the Greatest Common Factor of 1071 and 709?

The factors of 1071 are 1, 3, 7, 9, 17, 21, 51, 63, 119, 153, 357, 1071 and the factors of 709 are 1, 709. 1071 and 709 have only one common factor which is 1. This implies that 1071 and 709 are co-prime.

Hence, the Greatest Common Factor (GCF) of 1071 and 709 is 1.

How Many Factors of 791 are also common to the Factors of 1071?

Since, the factors of 1071 are 1, 3, 7, 9, 17, 21, 51, 63, 119, 153, 357, 1071 and the factors of 791 are 1, 7, 113, 791.
Hence, [1, 7] are the common factors of 1071 and 791.

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