Factor Calculator

Factors of 1005

The factors of 1005 are 1, 3, 5, 15, 67, 201, 335, and 1005. In total, 1005 has 8 factors. Its prime factorization is 3 × 5 × 67, and the sum of all its factors is 1632.

All factors of 1005

Here are all 8 factors of 1005, listed from smallest to largest.

13515672013351005

Factor pairs of 1005

These 4 pairs of whole numbers each multiply to give 1005.

1 × 1005 = 1005
3 × 335 = 1005
5 × 201 = 1005
15 × 67 = 1005

Prime factorization of 1005

Dividing 1005 by the smallest prime at each step gives its prime factorization:

1005 ÷ 3 = 335
335 ÷ 5 = 67
67 ÷ 67 = 1
Result: 1005 = 3 × 5 × 67 = 3 × 5 × 67

The distinct prime factors of 1005 are 3, 5, 67. To factorize any other number, use the prime factorization calculator.

Factor tree of 1005

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

Factor tree of 100510053335567
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 1005

Number of factors8
Sum of factors1632
Sum of proper factors627
Prime factorization3 × 5 × 67
Prime or composite?Composite
Even or odd?Odd
Perfect square?No
Perfect cube?No
ClassificationDeficient

What makes 1005 interesting

  • 1005 is a composite number, meaning it has more than two factors. It can be written as a product of smaller whole numbers in 4 different ways.
  • 1005 is a deficient number: its proper factors sum to 627, which is 378 less than 1005 itself.
  • 1005 has 3 distinct prime factors (3, 5, 67), which is why it has so many divisors.

How to find the factors of 1005 yourself

Divide 1005 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 √1005 ≈ 31.70, because every factor above that pairs with one below it.

1005 ÷ 1 = 1005 ✓
1005 ÷ 3 = 335 ✓
1005 ÷ 5 = 201 ✓
1005 ÷ 15 = 67 ✓

Reading both columns gives every factor: 1, 3, 5, 15, 67, 201, 335, 1005. The factor calculator does this automatically for any number.

Numbers mathematically connected to 1005.

Frequently asked questions about 1005

What are the factors of 1005?

The factors of 1005 are 1, 3, 5, 15, 67, 201, 335, and 1005. That is 8 factors in total, counting both 1 and 1005.

Is 1005 a prime number?

No, 1005 is not prime — it is a composite number with 8 factors. A prime number has exactly two factors, but 1005 is also divisible by 3.

What is the prime factorization of 1005?

The prime factorization of 1005 is 3 × 5 × 67. Written out in full: 3 × 5 × 67 = 1005. Its distinct prime factors are 3, 5, 67.

What two numbers multiply to give 1005?

There are 4 pairs of whole numbers that multiply to 1005: 1 × 1005, 3 × 335, 5 × 201, 15 × 67.

What is the sum of the factors of 1005?

Adding all the factors of 1005 together gives 1632. Excluding 1005 itself, the proper factors sum to 627.

Is 1005 a perfect square?

No, 1005 is not a perfect square. There is no whole number that multiplies by itself to give 1005. The nearest perfect squares are 961 and 1024.

What is the largest factor of 1005 other than itself?

The largest factor of 1005 apart from 1005 itself is 335, since 1005 ÷ 335 = 3.

How many factors does 1005 have?

1005 has 8 factors: 1, 3, 5, 15, 67, 201, 335, and 1005. You can verify this from the prime factorization 3 × 5 × 67: add 1 to each exponent and multiply, giving 2 × 2 × 2 = 8.

Explore more

Try another number in the factor calculator, break 1005 down further with the prime factorization calculator, or compare 1005 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.