Factor Calculator

Factors of 1200

The factors of 1200 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 150, 200, 240, 300, 400, 600, and 1200. In total, 1200 has 30 factors. Its prime factorization is 2⁴ × 3 × 5², and the sum of all its factors is 3844.

All factors of 1200

Here are all 30 factors of 1200, listed from smallest to largest.

123456810121516202425304048506075801001201502002403004006001200

Factor pairs of 1200

These 15 pairs of whole numbers each multiply to give 1200.

1 × 1200 = 1200
2 × 600 = 1200
3 × 400 = 1200
4 × 300 = 1200
5 × 240 = 1200
6 × 200 = 1200
8 × 150 = 1200
10 × 120 = 1200
12 × 100 = 1200
15 × 80 = 1200
16 × 75 = 1200
20 × 60 = 1200
24 × 50 = 1200
25 × 48 = 1200
30 × 40 = 1200

Prime factorization of 1200

Dividing 1200 by the smallest prime at each step gives its prime factorization:

1200 ÷ 2 = 600
600 ÷ 2 = 300
300 ÷ 2 = 150
150 ÷ 2 = 75
75 ÷ 3 = 25
25 ÷ 5 = 5
5 ÷ 5 = 1
Result: 1200 = 2 × 2 × 2 × 2 × 3 × 5 × 5 = 2⁴ × 3 × 5²

The distinct prime factors of 1200 are 2, 3, 5. To factorize any other number, use the prime factorization calculator.

Factor tree of 1200

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

Factor tree of 1200120026002300215027532555
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 1200

Number of factors30
Sum of factors3844
Sum of proper factors2644
Prime factorization2⁴ × 3 × 5²
Prime or composite?Composite
Even or odd?Even
Perfect square?No
Perfect cube?No
ClassificationAbundant

What makes 1200 interesting

  • 1200 is a composite number, meaning it has more than two factors. It can be written as a product of smaller whole numbers in 15 different ways.
  • 1200 is an abundant number: its proper factors sum to 2644, which is 1444 more than 1200 itself.
  • 1200 has 3 distinct prime factors (2, 3, 5), which is why it has so many divisors.

How to find the factors of 1200 yourself

Divide 1200 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 √1200 ≈ 34.64, because every factor above that pairs with one below it.

1200 ÷ 1 = 1200 ✓
1200 ÷ 2 = 600 ✓
1200 ÷ 3 = 400 ✓
1200 ÷ 4 = 300 ✓
1200 ÷ 5 = 240 ✓
1200 ÷ 6 = 200 ✓
1200 ÷ 8 = 150 ✓
1200 ÷ 10 = 120 ✓
1200 ÷ 12 = 100 ✓
1200 ÷ 15 = 80 ✓
1200 ÷ 16 = 75 ✓
1200 ÷ 20 = 60 ✓
1200 ÷ 24 = 50 ✓
1200 ÷ 25 = 48 ✓
1200 ÷ 30 = 40 ✓

Reading both columns gives every factor: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 150, 200, 240, 300, 400, 600, 1200. The factor calculator does this automatically for any number.

Numbers mathematically connected to 1200.

Frequently asked questions about 1200

What are the factors of 1200?

The factors of 1200 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 150, 200, 240, 300, 400, 600, and 1200. That is 30 factors in total, counting both 1 and 1200.

Is 1200 a prime number?

No, 1200 is not prime — it is a composite number with 30 factors. A prime number has exactly two factors, but 1200 is also divisible by 2.

What is the prime factorization of 1200?

The prime factorization of 1200 is 2⁴ × 3 × 5². Written out in full: 2 × 2 × 2 × 2 × 3 × 5 × 5 = 1200. Its distinct prime factors are 2, 3, 5.

What two numbers multiply to give 1200?

There are 15 pairs of whole numbers that multiply to 1200: 1 × 1200, 2 × 600, 3 × 400, 4 × 300, 5 × 240, 6 × 200, 8 × 150, 10 × 120, 12 × 100, 15 × 80, 16 × 75, 20 × 60, 24 × 50, 25 × 48, 30 × 40.

What is the sum of the factors of 1200?

Adding all the factors of 1200 together gives 3844. Excluding 1200 itself, the proper factors sum to 2644.

Is 1200 a perfect square?

No, 1200 is not a perfect square. There is no whole number that multiplies by itself to give 1200. The nearest perfect squares are 1156 and 1225.

What is the largest factor of 1200 other than itself?

The largest factor of 1200 apart from 1200 itself is 600, since 1200 ÷ 600 = 2.

How many factors does 1200 have?

1200 has 30 factors: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 150, 200, 240, 300, 400, 600, and 1200. You can verify this from the prime factorization 2⁴ × 3 × 5²: add 1 to each exponent and multiply, giving 5 × 2 × 3 = 30.

Explore more

Try another number in the factor calculator, break 1200 down further with the prime factorization calculator, or compare 1200 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.