Factor Calculator

Factors of 1050

The factors of 1050 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 25, 30, 35, 42, 50, 70, 75, 105, 150, 175, 210, 350, 525, and 1050. In total, 1050 has 24 factors. Its prime factorization is 2 × 3 × 5² × 7, and the sum of all its factors is 2976.

All factors of 1050

Here are all 24 factors of 1050, listed from smallest to largest.

12356710141521253035425070751051501752103505251050

Factor pairs of 1050

These 12 pairs of whole numbers each multiply to give 1050.

1 × 1050 = 1050
2 × 525 = 1050
3 × 350 = 1050
5 × 210 = 1050
6 × 175 = 1050
7 × 150 = 1050
10 × 105 = 1050
14 × 75 = 1050
15 × 70 = 1050
21 × 50 = 1050
25 × 42 = 1050
30 × 35 = 1050

Prime factorization of 1050

Dividing 1050 by the smallest prime at each step gives its prime factorization:

1050 ÷ 2 = 525
525 ÷ 3 = 175
175 ÷ 5 = 35
35 ÷ 5 = 7
7 ÷ 7 = 1
Result: 1050 = 2 × 3 × 5 × 5 × 7 = 2 × 3 × 5² × 7

The distinct prime factors of 1050 are 2, 3, 5, 7. To factorize any other number, use the prime factorization calculator.

Factor tree of 1050

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

Factor tree of 105010502525317553557
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 1050

Number of factors24
Sum of factors2976
Sum of proper factors1926
Prime factorization2 × 3 × 5² × 7
Prime or composite?Composite
Even or odd?Even
Perfect square?No
Perfect cube?No
ClassificationAbundant

What makes 1050 interesting

  • 1050 is a composite number, meaning it has more than two factors. It can be written as a product of smaller whole numbers in 12 different ways.
  • 1050 is an abundant number: its proper factors sum to 1926, which is 876 more than 1050 itself.
  • 1050 has 4 distinct prime factors (2, 3, 5, 7), which is why it has so many divisors.

How to find the factors of 1050 yourself

Divide 1050 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 √1050 ≈ 32.40, because every factor above that pairs with one below it.

1050 ÷ 1 = 1050 ✓
1050 ÷ 2 = 525 ✓
1050 ÷ 3 = 350 ✓
1050 ÷ 5 = 210 ✓
1050 ÷ 6 = 175 ✓
1050 ÷ 7 = 150 ✓
1050 ÷ 10 = 105 ✓
1050 ÷ 14 = 75 ✓
1050 ÷ 15 = 70 ✓
1050 ÷ 21 = 50 ✓
1050 ÷ 25 = 42 ✓
1050 ÷ 30 = 35 ✓

Reading both columns gives every factor: 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 25, 30, 35, 42, 50, 70, 75, 105, 150, 175, 210, 350, 525, 1050. The factor calculator does this automatically for any number.

Numbers mathematically connected to 1050.

Frequently asked questions about 1050

What are the factors of 1050?

The factors of 1050 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 25, 30, 35, 42, 50, 70, 75, 105, 150, 175, 210, 350, 525, and 1050. That is 24 factors in total, counting both 1 and 1050.

Is 1050 a prime number?

No, 1050 is not prime — it is a composite number with 24 factors. A prime number has exactly two factors, but 1050 is also divisible by 2.

What is the prime factorization of 1050?

The prime factorization of 1050 is 2 × 3 × 5² × 7. Written out in full: 2 × 3 × 5 × 5 × 7 = 1050. Its distinct prime factors are 2, 3, 5, 7.

What two numbers multiply to give 1050?

There are 12 pairs of whole numbers that multiply to 1050: 1 × 1050, 2 × 525, 3 × 350, 5 × 210, 6 × 175, 7 × 150, 10 × 105, 14 × 75, 15 × 70, 21 × 50, 25 × 42, 30 × 35.

What is the sum of the factors of 1050?

Adding all the factors of 1050 together gives 2976. Excluding 1050 itself, the proper factors sum to 1926.

Is 1050 a perfect square?

No, 1050 is not a perfect square. There is no whole number that multiplies by itself to give 1050. The nearest perfect squares are 1024 and 1089.

What is the largest factor of 1050 other than itself?

The largest factor of 1050 apart from 1050 itself is 525, since 1050 ÷ 525 = 2.

How many factors does 1050 have?

1050 has 24 factors: 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 25, 30, 35, 42, 50, 70, 75, 105, 150, 175, 210, 350, 525, and 1050. You can verify this from the prime factorization 2 × 3 × 5² × 7: add 1 to each exponent and multiply, giving 2 × 2 × 3 × 2 = 24.

Explore more

Try another number in the factor calculator, break 1050 down further with the prime factorization calculator, or compare 1050 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.