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Factors of 1125

Factors of 1125 are the list of integers that we can split evenly into 1125. There are overall 12 factors of 1125 among which 1125 is the biggest factor and 3, 5 are its prime factors. The Prime Factorization of 1125 is 32 × 53.

  • All Factors of 1125: 1, 3, 5, 9, 15, 25, 45, 75, 125, 225, 375 and 1125
  • Prime Factors of 1125: 3, 5
  • Prime Factorization of 1125: 32 × 53
  • Sum of Factors of 1125: 2028
1. What Are the Factors of 1125?
2. Factors of 1125 by Prime Factorization
3. Factors of 1125 in Pairs
4. FAQs on Factors of 1125
Factors of 1125

What are Factors of 1125?

Factors of 1125 are pairs of those numbers whose products result in 1125. These factors are either prime numbers or composite numbers.

How to Find the Factors of 1125?

To find the factors of 1125, we will have to find the list of numbers that would divide 1125 without leaving any remainder.

  • 1125/1 = 1125; therefore, 1 is a factor of 1125.
  • 1125/45 = 25; therefore, 45 is a factor of 1125.
Similarly we can find other factors. Hence, the factors of 1125 are 1, 3, 5, 9, 15, 25, 45, 75, 125, 225, 375, 1125.

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Factors of 1125 by Prime Factorization

The number 1125 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 1125. The first step is to divide the number 1125 with the smallest prime factor, here it is 3. We keep dividing until it gives a non-zero remainder.
  • 1125 ÷ 3 = 375
  • 375 ÷ 3 = 125

Further dividing 125 by 3 gives a non-zero remainder. So we stop the process and continue dividing the number 125 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 1125 can be written as 32 × 53 where 3, 5 are prime.

 

Factors of 1125 in Pairs

Pair factors of 1125 are the pairs of numbers that when multiplied give the product 1125. The factors of 1125 in pairs are:

  • 1 × 1125 = (1, 1125)
  • 3 × 375 = (3, 375)
  • 5 × 225 = (5, 225)
  • 9 × 125 = (9, 125)
  • 15 × 75 = (15, 75)
  • 25 × 45 = (25, 45)

Negative pair factors of 1125 are:

  • -1 × -1125 = (-1, -1125)
  • -3 × -375 = (-3, -375)
  • -5 × -225 = (-5, -225)
  • -9 × -125 = (-9, -125)
  • -15 × -75 = (-15, -75)
  • -25 × -45 = (-25, -45)

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

Factors of 1125 Solved Examples

  1. Example 1: How many factors are there for 1125?

    Solution:

    The factors of 1125 are too many, therefore if we can find the prime factorization of 1125, 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 1125 = 32 × 53
    Therefore, the total number of factors are (2 + 1) × (3 + 1) = 3 × 4 = 12

  2. Example 2: Find the Least Common Multiple (LCM) and Highest Common Factor (HCF) of 1125 and 727.

    Solution:

    The factors of 1125 are 1, 3, 5, 9, 15, 25, 45, 75, 125, 225, 375, 1125 and factors of 727 are 1, 727.

    Therefore, the Least Common Multiple (LCM) of 1125 and 727 is 817875 and Highest Common Factor (HCF) of 1125 and 727 is 1.

  3. Example 3: Find if 1, 3, 25, 125, 225, 621 and 1125 are factors of 1125.

    Solution:

    When we divide 1125 by 621 it leaves a remainder. Therefore, the number 621 is not a factor of 1125. All numbers except 621 are factors of 1125.

  4. Example 4: Find the product of all the prime factors of 1125.

    Solution:

    Since, the prime factors of 1125 are 3, 5. Therefore, the product of prime factors = 3 × 5 = 15.

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FAQs on Factors of 1125

What are the Factors of 1125?

The factors of 1125 are 1, 3, 5, 9, 15, 25, 45, 75, 125, 225, 375, 1125 and its negative factors are -1, -3, -5, -9, -15, -25, -45, -75, -125, -225, -375, -1125.

What is the Sum of Factors of 1125?

Sum of all factors of 1125 = (32 + 1 - 1)/(3 - 1) × (53 + 1 - 1)/(5 - 1) = 2028

What numbers are the Pair Factors of 1125?

The pair factors of 1125 are (1, 1125), (3, 375), (5, 225), (9, 125), (15, 75), (25, 45).

What is the Greatest Common Factor of 1125 and 1049?

The factors of 1125 are 1, 3, 5, 9, 15, 25, 45, 75, 125, 225, 375, 1125 and the factors of 1049 are 1, 1049. 1125 and 1049 have only one common factor which is 1. This implies that 1125 and 1049 are co-prime.

Hence, the Greatest Common Factor (GCF) of 1125 and 1049 is 1.

How Many Factors of 1125 are also common to the Factors of 912?

Since, the factors of 1125 are 1, 3, 5, 9, 15, 25, 45, 75, 125, 225, 375, 1125 and the factors of 912 are 1, 2, 3, 4, 6, 8, 12, 16, 19, 24, 38, 48, 57, 76, 114, 152, 228, 304, 456, 912.
Hence, [1, 3] are the common factors of 1125 and 912.

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