Factor Calculator

Factors of 448

The factors of 448 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 224, and 448. In total, 448 has 14 factors. Its prime factorization is 2⁶ × 7, and the sum of all its factors is 1016.

All factors of 448

Here are all 14 factors of 448, listed from smallest to largest.

12478141628325664112224448

Factor pairs of 448

These 7 pairs of whole numbers each multiply to give 448.

1 × 448 = 448
2 × 224 = 448
4 × 112 = 448
7 × 64 = 448
8 × 56 = 448
14 × 32 = 448
16 × 28 = 448

Prime factorization of 448

Dividing 448 by the smallest prime at each step gives its prime factorization:

448 ÷ 2 = 224
224 ÷ 2 = 112
112 ÷ 2 = 56
56 ÷ 2 = 28
28 ÷ 2 = 14
14 ÷ 2 = 7
7 ÷ 7 = 1
Result: 448 = 2 × 2 × 2 × 2 × 2 × 2 × 7 = 2⁶ × 7

The distinct prime factors of 448 are 2, 7. To factorize any other number, use the prime factorization calculator.

Factor tree of 448

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

Factor tree of 4484482224211225622821427
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 448

Number of factors14
Sum of factors1016
Sum of proper factors568
Prime factorization2⁶ × 7
Prime or composite?Composite
Even or odd?Even
Perfect square?No
Perfect cube?No
ClassificationAbundant

What makes 448 interesting

  • 448 is a composite number, meaning it has more than two factors. It can be written as a product of smaller whole numbers in 7 different ways.
  • 448 is an abundant number: its proper factors sum to 568, which is 120 more than 448 itself.

How to find the factors of 448 yourself

Divide 448 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 √44821.17, because every factor above that pairs with one below it.

448 ÷ 1 = 448
448 ÷ 2 = 224
448 ÷ 4 = 112
448 ÷ 7 = 64
448 ÷ 8 = 56
448 ÷ 14 = 32
448 ÷ 16 = 28

Reading both columns gives every factor: 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 224, 448. The factor calculator does this automatically for any number.

Frequently asked questions about 448

What are the factors of 448?

The factors of 448 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 224, and 448. That is 14 factors in total, counting both 1 and 448.

Is 448 a prime number?

No, 448 is not prime — it is a composite number with 14 factors. A prime number has exactly two factors, but 448 is also divisible by 2.

What is the prime factorization of 448?

The prime factorization of 448 is 2⁶ × 7. Written out in full: 2 × 2 × 2 × 2 × 2 × 2 × 7 = 448. Its distinct prime factors are 2, 7.

What two numbers multiply to give 448?

There are 7 pairs of whole numbers that multiply to 448: 1 × 448, 2 × 224, 4 × 112, 7 × 64, 8 × 56, 14 × 32, 16 × 28.

What is the sum of the factors of 448?

Adding all the factors of 448 together gives 1016. Excluding 448 itself, the proper factors sum to 568.

Is 448 a perfect square?

No, 448 is not a perfect square. There is no whole number that multiplies by itself to give 448. The nearest perfect squares are 441 and 484.

What is the largest factor of 448 other than itself?

The largest factor of 448 apart from 448 itself is 224, since 448 ÷ 224 = 2.

How many factors does 448 have?

448 has 14 factors: 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 224, and 448. You can verify this from the prime factorization 2⁶ × 7: add 1 to each exponent and multiply, giving 7 × 2 = 14.

Explore more

Try another number in the factor calculator, break 448 down further with the prime factorization calculator, or compare 448 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.