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Factors of 1110

Factors of 1110 are integers that can be divided evenly into 1110. There are overall 16 factors of 1110 among which 1110 is the biggest factor and 2, 3, 5, 37 are its prime factors. The Prime Factorization of 1110 is 21 × 31 × 51 × 371.

  • All Factors of 1110: 1, 2, 3, 5, 6, 10, 15, 30, 37, 74, 111, 185, 222, 370, 555 and 1110
  • Prime Factors of 1110: 2, 3, 5, 37
  • Prime Factorization of 1110: 21 × 31 × 51 × 371
  • Sum of Factors of 1110: 2736
1. What Are the Factors of 1110?
2. Factors of 1110 by Prime Factorization
3. Factors of 1110 in Pairs
4. FAQs on Factors of 1110
Factors of 1110

What are Factors of 1110?

Factors of 1110 are pairs of those numbers whose products result in 1110. These factors are either prime numbers or composite numbers.

How to Find the Factors of 1110?

To find the factors of 1110, we will have to find the list of numbers that would divide 1110 without leaving any remainder.

  • 1110/370 = 3; therefore, 370 is a factor of 1110 and 3 is also a factor of 1110.
  • 1110/15 = 74; therefore, 15 is a factor of 1110 and 74 is also a factor of 1110.
Similarly we can find other factors. Hence, the factors of 1110 are 1, 2, 3, 5, 6, 10, 15, 30, 37, 74, 111, 185, 222, 370, 555, 1110.

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Factors of 1110 by Prime Factorization

The number 1110 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 1110. The first step is to divide the number 1110 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.
  • 1110 ÷ 2 = 555

Further dividing 555 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 555 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 1110 can be written as 21 × 31 × 51 × 371 where 2, 3, 5, 37 are prime.

 

Factors of 1110 in Pairs

Pair factors of 1110 are the pairs of numbers that when multiplied give the product 1110. The factors of 1110 in pairs are:

  • 1 × 1110 = (1, 1110)
  • 2 × 555 = (2, 555)
  • 3 × 370 = (3, 370)
  • 5 × 222 = (5, 222)
  • 6 × 185 = (6, 185)
  • 10 × 111 = (10, 111)
  • 15 × 74 = (15, 74)
  • 30 × 37 = (30, 37)

Negative pair factors of 1110 are:

  • -1 × -1110 = (-1, -1110)
  • -2 × -555 = (-2, -555)
  • -3 × -370 = (-3, -370)
  • -5 × -222 = (-5, -222)
  • -6 × -185 = (-6, -185)
  • -10 × -111 = (-10, -111)
  • -15 × -74 = (-15, -74)
  • -30 × -37 = (-30, -37)

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

Factors of 1110 Solved Examples

  1. Example 1: How many factors are there for 1110?

    Solution:

    The factors of 1110 are too many, therefore if we can find the prime factorization of 1110, 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 1110 = 21 × 31 × 51 × 371
    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 Least Common Multiple and Greatest Common Divisor (GCD) of 1110 and 370.

    Solution:

    The factors of 1110 are 1, 2, 3, 5, 6, 10, 15, 30, 37, 74, 111, 185, 222, 370, 555, 1110 and factors of 370 are 1, 2, 5, 10, 37, 74, 185, 370.

    Therefore, the Least Common Multiple of 1110 and 370 is 1110 and Greatest Common Divisor (GCD) of 1110 and 370 is 370.

  3. Example 3: Find if 2, 3, 5, 37, 185, 555, 697 and 1110 are factors of 1110.

    Solution:

    When we divide 1110 by 697 it leaves a remainder. Therefore, the number 697 is not a factor of 1110. All numbers except 697 are factors of 1110.

  4. Example 4: Find the product of all the prime factors of 1110.

    Solution:

    Since, the prime factors of 1110 are 2, 3, 5, 37. Therefore, the product of prime factors = 2 × 3 × 5 × 37 = 1110.

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FAQs on Factors of 1110

What are the Factors of 1110?

The factors of 1110 are 1, 2, 3, 5, 6, 10, 15, 30, 37, 74, 111, 185, 222, 370, 555, 1110 and its negative factors are -1, -2, -3, -5, -6, -10, -15, -30, -37, -74, -111, -185, -222, -370, -555, -1110.

What is the Sum of all the Factors of 1110?

Sum of all factors of 1110 = (21 + 1 - 1)/(2 - 1) × (31 + 1 - 1)/(3 - 1) × (51 + 1 - 1)/(5 - 1) × (371 + 1 - 1)/(37 - 1) = 2736

What are Pair Factors of 1110?

The pair factors of 1110 are (1, 1110), (2, 555), (3, 370), (5, 222), (6, 185), (10, 111), (15, 74), (30, 37).

What is the Greatest Common Factor of 1110 and 557?

The factors of 1110 are 1, 2, 3, 5, 6, 10, 15, 30, 37, 74, 111, 185, 222, 370, 555, 1110 and the factors of 557 are 1, 557. 1110 and 557 have only one common factor which is 1. This implies that 1110 and 557 are co-prime.

Hence, the Greatest Common Factor (GCF) of 1110 and 557 is 1.

How Many Factors of 551 are also common to the Factors of 1110?

Since, the factors of 1110 are 1, 2, 3, 5, 6, 10, 15, 30, 37, 74, 111, 185, 222, 370, 555, 1110 and factors of 551 are 1, 19, 29, 551. Hence, 1110 and 551 have only one common factor which is 1. Therefore, 1110 and 551 are co-prime.

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