Find the prime factorization of each number?

Question

525

Answer 1

525=3*5^2*7

Answer 2

Any whole number bigger than 1 can be represented in exactly one way as a product of primes. This theorem is called the Fundamental Theorem of Arithmetic, and it is also called the Unique Factorization Theorem.


You will need to know this on a test, so
To prime factor a number, begin dividing by the smallest possible prime and continue until the quotient is a prime number.

What is a prime number?

A prime number is a positive integer that has exactly two positive integer factors, 1 and itself. For example, if we list the factors of 28, we have 1, 2, 4, 7, 14, and 28. That's six factors. If we list the factors of 29, we only have 1 and 29. That's two factors. So we say that 29 is a prime number, but 28 isn't.
Another way of saying this is that a prime number is a positive integer that is not the product of two smaller positive integers.

Note that the definition of a prime number doesn't allow 1 to be a prime number: 1 only has one factor, namely 1. Prime numbers have exactly two factors, not "at most two" or anything like that. When a number has more than two factors it is called a composite number.

Here are the first few prime numbers:


2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, etc.



we can write

525 = 3 × 5^2 × 7,

and any other factorization of 525 as the product of primes will be identical except for the order of the factors.

Please take time to learn this: Math can open many doors.

Take a look at these sites to learn how to do factorization step by step.
http://www.purplemath.com/modules/factnumb.htm

I hope this helps

Answer 3

525 = 5*105 = 5*5*21 = 3*5*5*7