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Factors of 1155

Factors of 1155 are the list of integers that we can split evenly into 1155. There are overall 16 factors of 1155 among which 1155 is the biggest factor and 3, 5, 7, 11 are its prime factors. The sum of all factors of 1155 is 2304.

  • All Factors of 1155: 1, 3, 5, 7, 11, 15, 21, 33, 35, 55, 77, 105, 165, 231, 385 and 1155
  • Prime Factors of 1155: 3, 5, 7, 11
  • Prime Factorization of 1155: 31 × 51 × 71 × 111
  • Sum of Factors of 1155: 2304
1. What Are the Factors of 1155?
2. Factors of 1155 by Prime Factorization
3. Factors of 1155 in Pairs
4. FAQs on Factors of 1155
Factors of 1155

What are Factors of 1155?

Factors of 1155 are pairs of those numbers whose products result in 1155. These factors are either prime numbers or composite numbers.

How to Find the Factors of 1155?

To find the factors of 1155, we will have to find the list of numbers that would divide 1155 without leaving any remainder.

  • 1155/7 = 165; therefore, 7 is a factor of 1155 and 165 is also a factor of 1155.
  • 1155/15 = 77; therefore, 15 is a factor of 1155 and 77 is also a factor of 1155.
Similarly we can find other factors. Hence, the factors of 1155 are 1, 3, 5, 7, 11, 15, 21, 33, 35, 55, 77, 105, 165, 231, 385, 1155.

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Factors of 1155 by Prime Factorization

The number 1155 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 1155. The first step is to divide the number 1155 with the smallest prime factor, here it is 3. We keep dividing until it gives a non-zero remainder.
  • 1155 ÷ 3 = 385

Further dividing 385 by 3 gives a non-zero remainder. So we stop the process and continue dividing the number 385 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 1155 can be written as 31 × 51 × 71 × 111 where 3, 5, 7, 11 are prime.

 

Factors of 1155 in Pairs

Pair factors of 1155 are the pairs of numbers that when multiplied give the product 1155. The factors of 1155 in pairs are:

  • 1 × 1155 = (1, 1155)
  • 3 × 385 = (3, 385)
  • 5 × 231 = (5, 231)
  • 7 × 165 = (7, 165)
  • 11 × 105 = (11, 105)
  • 15 × 77 = (15, 77)
  • 21 × 55 = (21, 55)
  • 33 × 35 = (33, 35)

Negative pair factors of 1155 are:

  • -1 × -1155 = (-1, -1155)
  • -3 × -385 = (-3, -385)
  • -5 × -231 = (-5, -231)
  • -7 × -165 = (-7, -165)
  • -11 × -105 = (-11, -105)
  • -15 × -77 = (-15, -77)
  • -21 × -55 = (-21, -55)
  • -33 × -35 = (-33, -35)

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

Factors of 1155 Solved Examples

  1. Example 1: How many factors are there for 1155?

    Solution:

    The factors of 1155 are too many, therefore if we can find the prime factorization of 1155, 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 1155 = 31 × 51 × 71 × 111
    Therefore, the total number of factors are (1 + 1) × (1 + 1) × (1 + 1) × (1 + 1) = 2 × 2 × 2 × 2 = 16

  2. Example 2: Find the LCM and Greatest Common Divisor (GCD) of 1155 and 1066.

    Solution:

    The factors of 1155 are 1, 3, 5, 7, 11, 15, 21, 33, 35, 55, 77, 105, 165, 231, 385, 1155 and factors of 1066 are 1, 2, 13, 26, 41, 82, 533, 1066.

    Therefore, the LCM of 1155 and 1066 is 1231230 and Greatest Common Divisor (GCD) of 1155 and 1066 is 1.

  3. Example 3: Find if 1, 5, 7, 15, 154, 165, 231 and 385 are factors of 1155.

    Solution:

    When we divide 1155 by 154 it leaves a remainder. Therefore, the number 154 is not a factor of 1155. All numbers except 154 are factors of 1155.

  4. Example 4: Find the product of all the prime factors of 1155.

    Solution:

    Since, the prime factors of 1155 are 3, 5, 7, 11. Therefore, the product of prime factors = 3 × 5 × 7 × 11 = 1155.

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FAQs on Factors of 1155

What are the Factors of 1155?

The factors of 1155 are 1, 3, 5, 7, 11, 15, 21, 33, 35, 55, 77, 105, 165, 231, 385, 1155 and its negative factors are -1, -3, -5, -7, -11, -15, -21, -33, -35, -55, -77, -105, -165, -231, -385, -1155.

What is the Sum of Factors of 1155?

Sum of all factors of 1155 = (31 + 1 - 1)/(3 - 1) × (51 + 1 - 1)/(5 - 1) × (71 + 1 - 1)/(7 - 1) × (111 + 1 - 1)/(11 - 1) = 2304

What are Prime Factors of 1155?

The prime factors of 1155 are 3, 5, 7, 11.

What is the Greatest Common Factor of 1155 and 68?

The factors of 1155 are 1, 3, 5, 7, 11, 15, 21, 33, 35, 55, 77, 105, 165, 231, 385, 1155 and the factors of 68 are 1, 2, 4, 17, 34, 68. 1155 and 68 have only one common factor which is 1. This implies that 1155 and 68 are co-prime.

Hence, the Greatest Common Factor (GCF) of 1155 and 68 is 1.

How Many Factors of 1155 are also common to the Factors of 90?

Since, the factors of 1155 are 1, 3, 5, 7, 11, 15, 21, 33, 35, 55, 77, 105, 165, 231, 385, 1155 and the factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90.
Hence, [1, 3, 5, 15] are the common factors of 1155 and 90.

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