The prime factorization of 441 is the process of breaking down the number 441 into its prime numbers. Prime factorization is important in various fields of mathematics, including number theory and cryptography.
To find the prime factorization of 441, follow these steps:
- Divide 441 by the smallest prime number, which is 3. 441 ÷ 3 = 147.
- Now, divide 147 by 3 again. 147 ÷ 3 = 49.
- Next, divide 49 by 7, which is also a prime number. 49 ÷ 7 = 7.
- Finally, divide 7 by itself. 7 ÷ 7 = 1.
So, the prime factors of 441 are 3, 3, 7, and 7. This can be written as:
441 = 3 × 3 × 7 × 7
Or, using exponents:
441 = 3² × 7²
This is the prime factorization of 441.