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Q:

# What is the prime factorization of 200?

A:

The prime factorization of 200 is 2 x 2 x 2 x 5 x 5, which is written using exponents as 2^3 x 5^2. Prime factorization involves finding the prime numbers that multiply together to make a particular number.

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Prime numbers are numbers that are evenly divisible by only one and themselves. Composite numbers, such as the number 200, have other factors as well. Find two factors of 200, such as 40 x 5. Five is a prime number, but 40 is not. Find two factors of 40, such as 8 x 5. Again, five is prime, but eight is not. Eight equals 4 x 2. Two is prime, but four is a composite equal to 2 x 2. The prime numbers then that multiply together to make 200 are thee twos and two fives.

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The prime factorization of 81 is 3 x 3 x 3 x 3, or 3 ^ 4. Prime factorization of a number involves finding the prime numbers that, when multiplied together, yield that number.

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The prime factorization of 38 is 19 multiplied by 2. Prime factorization involves finding which prime numbers may be multiplied together to yield a particular number. Prime numbers are numbers greater than one that are only divisible by one and themselves.

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The prime factors of 55 are 5 and 11. Prime factorization means finding the prime numbers that can be multiplied together to produce the original number. The other factors of 55 are 1 and 55, but since neither are prime, they are not considered prime factors.