Prime factors of 735

The prime factors are: 3, 5, 7, 7
Prime Factor Decomposition or Prime Factorization is the process of finding which prime numbers can be multiplied together to make the original number. 735 divided by 3, 5, 7, 7 gives no remainder. This means Prime number are numbers that can divide without remainder.

How to Calculate Prime Factorization of 735?

The main method of prime factorization is start dividing the number by the any divisible prime numbers until the only numbers left are prime numbers \( (2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, ...) \).

\(735\div \color{red}{3} = 245\)
\(245\div \color{red}{5} = 49\)
\(49\div \color{red}{7} = 7\)
\(7\div \color{red}{7} = 1\)

Factorize\( (735) = \) \(3\times 5\times 7\times 7\)