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------------------------------------------------ Write the prime factorization of the following numbers:

(a) 735

(b) 7000

Answer :

Final answer:

The prime factorization for 735 is 3*5*7^2 and for 7000 is 2^3 * 5^3 * 7.

Explanation:

The prime factorization of a number is breaking it down into its smallest constituent prime factors. We do this by repeatedly dividing by prime numbers until we can't anymore.

  1. For 735: Start dividing 735 by the smallest prime number 2, but since 735 is odd, move to the next prime number 3. 735 is not divisible by 3, so try the next prime number 5. It is divisible now. Repeat the process until you get a prime number.
  2. The prime factorization of 735 is 3*5*7*7 or 3*5*7^2.
  3. For 7000: This time it is divisible by 2. Continue the process until you get a prime number.
  4. The prime factorization of 7000 is 2^3 * 5^3 * 7.

So, the prime factorization for 735 is 3*5*7^2 and for 7000 is 2^3 * 5^3 * 7.

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