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All composite numbers can be expressed as unique products of prime numbers. This is accomplished by dividing the original number and its factors by prime numbers until all the factors are prime. A factor tree can help you visualize this.
Example: 210
210 Divide by two.
105,2 Divide by three.
35,3,2 Divide by five.
7,5,3,2 Stop. All the factors are prime.
2 x 3 x 5 x 7 = 210
That's the prime factorization of 210.
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What are the factors for number 65?
To find the factors of a number you should first break that number down into its prime factors. In this case 65 can be broken down as: 65 = 5x13 To find any other factors, you then multiply any combination of these prime factors together. In this case, the factors of 65 come out as: 1, 5, 13 and 65.
What does prime factorization have to do with exponents?
Once you break a number down to prime factors, you can group together the factors that are the same. For example,... 200 = 2 * 2 * 2 * 5 * 5 = 23 * 52
What are the factors for number 66?
The first step to finding the factors of a number is to break the number down into its prime factors. In this case, 66 can be broken down as follows: 66 = 2x3x11 To find the other factors (apart from one) you have to multiply any combination of these prime factors together. That gives us the factors of 66 as: 1, 2, 3, 6, 11, 22, 33, 66.
How can you break down numbers?
The best way to break down a number (from the perspective of arithmetic!) is to write it as a product of its prime factors. For instance, 24 = 2 x 3 x 4 where x is the multiplication operator and of course 2, 3, and 4 are all prime numbers.
What is the largest number less than 100 that is relatively prime to 170?
A number is relatively prime to a number if it has no common prime factors with that number. To calculate relative primes, we need to break 170 down into its prime factors. These are: 2, 5, 17. Thus we want to find a number that is made up solely from multiplying 3s, 7s, 11s, 13s, 19s, 23s, 29s and 31s together. The largest number less than 100 that meets this criteria is 99, which has prime factors of 3, 3 and 11.
