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Factors of 825

Factors of 825 are numbers that, when multiplied in pairs give the product as 825. There are overall 12 factors of 825 among which 825 is the biggest factor and its prime factors are 3, 5, 11. The sum of all factors of 825 is 1488.

  • All Factors of 825: 1, 3, 5, 11, 15, 25, 33, 55, 75, 165, 275 and 825
  • Prime Factors of 825: 3, 5, 11
  • Prime Factorization of 825: 31 × 52 × 111
  • Sum of Factors of 825: 1488
1. What Are the Factors of 825?
2. Factors of 825 by Prime Factorization
3. Factors of 825 in Pairs
4. FAQs on Factors of 825
Factors of 825

What are Factors of 825?

Factors of 825 are pairs of those numbers whose products result in 825. These factors are either prime numbers or composite numbers.

How to Find the Factors of 825?

To find the factors of 825, we will have to find the list of numbers that would divide 825 without leaving any remainder.

  • 825/825 = 1; therefore, 825 is a factor of 825.
  • 825/3 = 275; therefore, 3 is a factor of 825.
Similarly we can find other factors. Hence, the factors of 825 are 1, 3, 5, 11, 15, 25, 33, 55, 75, 165, 275, 825.

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Factors of 825 by Prime Factorization

The number 825 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 825. The first step is to divide the number 825 with the smallest prime factor, here it is 3. We keep dividing until it gives a non-zero remainder.
  • 825 ÷ 3 = 275

Further dividing 275 by 3 gives a non-zero remainder. So we stop the process and continue dividing the number 275 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 825 can be written as 31 × 52 × 111 where 3, 5, 11 are prime.

 

Factors of 825 in Pairs

Pair factors of 825 are the pairs of numbers that when multiplied give the product 825. The factors of 825 in pairs are:

  • 1 × 825 = (1, 825)
  • 3 × 275 = (3, 275)
  • 5 × 165 = (5, 165)
  • 11 × 75 = (11, 75)
  • 15 × 55 = (15, 55)
  • 25 × 33 = (25, 33)

Negative pair factors of 825 are:

  • -1 × -825 = (-1, -825)
  • -3 × -275 = (-3, -275)
  • -5 × -165 = (-5, -165)
  • -11 × -75 = (-11, -75)
  • -15 × -55 = (-15, -55)
  • -25 × -33 = (-25, -33)

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

Factors of 825 Solved Examples

  1. Example 1: How many factors are there for 825?

    Solution:

    The factors of 825 are too many, therefore if we can find the prime factorization of 825, 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 825 = 31 × 52 × 111
    Therefore, the total number of factors are (1 + 1) × (2 + 1) × (1 + 1) = 2 × 3 × 2 = 12

  2. Example 2: Find the Least Common Multiple (LCM) and Greatest Common Factor (GCF) of 825 and 296.

    Solution:

    The factors of 825 are 1, 3, 5, 11, 15, 25, 33, 55, 75, 165, 275, 825 and factors of 296 are 1, 2, 4, 8, 37, 74, 148, 296.

    Therefore, the Least Common Multiple (LCM) of 825 and 296 is 244200 and Greatest Common Factor (GCF) of 825 and 296 is 1.

  3. Example 3: Find if 3, 11, 33, 55, 165, 275 and 703 are factors of 825.

    Solution:

    When we divide 825 by 703 it leaves a remainder. Therefore, the number 703 is not a factor of 825. All numbers except 703 are factors of 825.

  4. Example 4: Find the product of all the prime factors of 825.

    Solution:

    Since, the prime factors of 825 are 3, 5, 11. Therefore, the product of prime factors = 3 × 5 × 11 = 165.

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FAQs on Factors of 825

What are the Factors of 825?

The factors of 825 are 1, 3, 5, 11, 15, 25, 33, 55, 75, 165, 275, 825 and its negative factors are -1, -3, -5, -11, -15, -25, -33, -55, -75, -165, -275, -825.

What is the Sum of all the Factors of 825?

Sum of all factors of 825 = (31 + 1 - 1)/(3 - 1) × (52 + 1 - 1)/(5 - 1) × (111 + 1 - 1)/(11 - 1) = 1488

What numbers are the Pair Factors of 825?

The pair factors of 825 are (1, 825), (3, 275), (5, 165), (11, 75), (15, 55), (25, 33).

What is the Greatest Common Factor of 825 and 161?

The factors of 825 are 1, 3, 5, 11, 15, 25, 33, 55, 75, 165, 275, 825 and the factors of 161 are 1, 7, 23, 161. 825 and 161 have only one common factor which is 1. This implies that 825 and 161 are co-prime.

Hence, the Greatest Common Factor (GCF) of 825 and 161 is 1.

How Many Factors of 825 are also common to the Factors of 665?

Since, the factors of 825 are 1, 3, 5, 11, 15, 25, 33, 55, 75, 165, 275, 825 and the factors of 665 are 1, 5, 7, 19, 35, 95, 133, 665.
Hence, [1, 5] are the common factors of 825 and 665.

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