Calculators

Math

Factors

144 is a perfect square (12²) known as a gross (a dozen dozens). It's the largest square in the Fibonacci sequence and has 15 factors.

All Factors

The factors of 144 are:  1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144

The prime factorization is: 144 = 2 x 2 x 2 x 2 x 3 x 3

Factoring of 144 Using Trial Division

Find the Factors of 144 :

• Calculate the square root of 144 which is 12, and round it down to the closest whole number, 12, and use it in the next step.
• Test the integer values 1 through 12 for division into 144 where the remainder equals 0.
• We find 15 factors where the remainder of division is 0 and they are: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144.

Factor Pairs

1 × 144 = 144
2 × 72 = 144
3 × 48 = 144
4 × 36 = 144
6 × 24 = 144
8 × 18 = 144
9 × 16 = 144
12 × 12 = 144

The factor pairs (multiples) that equal 144 when multiplied together are: (1 and 144), (2 and 72), (3 and 48), (4 and 36), (6 and 24), (8 and 18), (9 and 16), (12 and 12), which we found by matching up all factors of 144 which are: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144.

Is 144 Prime or Composite?

144 is a composite number. Since it has more than two factors, we know that 144 is not prime, it is composite. Prime numbers only have two factors. They are evenly divisible by only 1 and itself.

Is 144 a Perfect Square?

Yes! Since the square root of 144 is an integer, 12, this tells us that 144 is a perfect square. It is a perfect square of 12 because 12 multiplied by itself or 12² equals 144.