Prime Factorization Calculator
Answer |
▶ Prime Factors of 68:
2, 2, 17
▶ Complete prime factorization:
\(68 = 2 × 2 × 17 = \) \(2^2\) × \(17^1\)
▶ Prime factorization tree:
68
↓ ↘
34 2
↓ ↘
17 2
Factoring a Number Into Prime Factors
Every natural number greater than one has several divisors and can be represented as a product of its divisors.
21 = 3 x 7 54 = 6 x 9
Representing a number as a product of natural numbers is called decomposition into multipliers. The multipliers can be simple or composite numbers.
42 = 2 x 3 x 7 36 = 4 x 9
The representation of a composite number as a product, all of whose factors are prime numbers, is called the prime factorization of the number.
\[ 36 = 2^2 \times 3^2 \] \[ 60 = 2^2 \times 3 \times 5 \]
To factor a number into its prime factors, the following algorithms can be used.
Method 1
Write the number as a product of two arbitrary multipliers. If one of the multipliers is a composite number, factor it again, and so on. We continue the factorization until we obtain only prime factors.
20 = 2 x 2 x 5 48 = 2 x 2 x 2 x 2 x 3
Method 2
Decompose the composite number into prime factors using the signs of divisibility.
Draw a vertical line and write the divisor to the left of it and the smallest prime divisor of the number to the right. Write the particle to the left of the risk under the divisor. Write each successive divisor under the previous one in ascending order.
