Factor Calculator

Factors of 825

The factors of 825 are 1, 3, 5, 11, 15, 25, 33, 55, 75, 165, 275, and 825. In total, 825 has 12 factors. Its prime factorization is 3 × 5² × 11, and the sum of all its factors is 1488.

All factors of 825

Here are all 12 factors of 825, listed from smallest to largest.

135111525335575165275825

Factor pairs of 825

These 6 pairs of whole numbers each multiply to give 825.

1 × 825 = 825
3 × 275 = 825
5 × 165 = 825
11 × 75 = 825
15 × 55 = 825
25 × 33 = 825

Prime factorization of 825

Dividing 825 by the smallest prime at each step gives its prime factorization:

825 ÷ 3 = 275
275 ÷ 5 = 55
55 ÷ 5 = 11
11 ÷ 11 = 1
Result: 825 = 3 × 5 × 5 × 11 = 3 × 5² × 11

The distinct prime factors of 825 are 3, 5, 11. To factorize any other number, use the prime factorization calculator.

Factor tree of 825

A factor tree shows the same prime factorization visually. Each composite branch splits until every endpoint is a prime number.

Factor tree of 8258253275555511
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 825

Number of factors12
Sum of factors1488
Sum of proper factors663
Prime factorization3 × 5² × 11
Prime or composite?Composite
Even or odd?Odd
Perfect square?No
Perfect cube?No
ClassificationDeficient

What makes 825 interesting

  • 825 is a composite number, meaning it has more than two factors. It can be written as a product of smaller whole numbers in 6 different ways.
  • 825 is a deficient number: its proper factors sum to 663, which is 162 less than 825 itself.
  • 825 has 3 distinct prime factors (3, 5, 11), which is why it has so many divisors.

How to find the factors of 825 yourself

Divide 825 by each whole number starting from 1. Whenever the division leaves no remainder, both the divisor and the quotient are factors. You only need to test up to √825 ≈ 28.72, because every factor above that pairs with one below it.

825 ÷ 1 = 825 ✓
825 ÷ 3 = 275 ✓
825 ÷ 5 = 165 ✓
825 ÷ 11 = 75 ✓
825 ÷ 15 = 55 ✓
825 ÷ 25 = 33 ✓

Reading both columns gives every factor: 1, 3, 5, 11, 15, 25, 33, 55, 75, 165, 275, 825. The factor calculator does this automatically for any number.

Numbers mathematically connected to 825.

Frequently asked questions about 825

What are the factors of 825?

The factors of 825 are 1, 3, 5, 11, 15, 25, 33, 55, 75, 165, 275, and 825. That is 12 factors in total, counting both 1 and 825.

Is 825 a prime number?

No, 825 is not prime — it is a composite number with 12 factors. A prime number has exactly two factors, but 825 is also divisible by 3.

What is the prime factorization of 825?

The prime factorization of 825 is 3 × 5² × 11. Written out in full: 3 × 5 × 5 × 11 = 825. Its distinct prime factors are 3, 5, 11.

What two numbers multiply to give 825?

There are 6 pairs of whole numbers that multiply to 825: 1 × 825, 3 × 275, 5 × 165, 11 × 75, 15 × 55, 25 × 33.

What is the sum of the factors of 825?

Adding all the factors of 825 together gives 1488. Excluding 825 itself, the proper factors sum to 663.

Is 825 a perfect square?

No, 825 is not a perfect square. There is no whole number that multiplies by itself to give 825. The nearest perfect squares are 784 and 841.

What is the largest factor of 825 other than itself?

The largest factor of 825 apart from 825 itself is 275, since 825 ÷ 275 = 3.

How many factors does 825 have?

825 has 12 factors: 1, 3, 5, 11, 15, 25, 33, 55, 75, 165, 275, and 825. You can verify this from the prime factorization 3 × 5² × 11: add 1 to each exponent and multiply, giving 2 × 3 × 2 = 12.

Explore more

Try another number in the factor calculator, break 825 down further with the prime factorization calculator, or compare 825 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.