Arithmetic Definitions

Arithmetic Definitions
A prime number (or prime integer, often simply called a "prime" for short) is a positive integer  that has no positive integer divisors other than 1 and  itself. 
A compositenumber  is a positive integer  which is not prime (i.e., which hasfactors other than 1 and itself). The first few composite numbers (sometimes called "composites" for short) are 4, 6, 8, 9, 10, 12,14, 15, 16.
Divisibility criteria of 2: If the last digit is 0, 2, 4, 6, or 8, then 2 goes into the number.
Divisibility criteria of 3: If the sum of the digits is divisible by 3, then the number isdivisible by 3. This also works for 9. If the sum of the digits is divisible by 9 then the number is divisible by 9. However, this method will not work for 6. 36 is divisible by 6 even though the sumof the digits, 9, is not, and 15 is not divisible by 6 even though the sum of the digits is 6.
Divisibility criteria of 5: If the last digit is 0 or 5, then the number is divisible by 5.
To write anumber as a product of prime numbers, we can use a factor ladder.
For example for number 120:
2 | 120 |
2 | 60 |
2 | 30 |
3 | 15 |
5 | 5 |
1 | |

So the prime factorization would be:23 x 3 x 5.

For number 72:
72 | 2 |
36 | 2 |
18 | 2 |
9 | 3 |
3 | 3 |
1 | | | |
| | | |
So the prime factorization would be: 23 x 32.
And for number 150:
150 | 2 |
75 | 3|
25 | 5 |
5 | 5 |
1 | |

So the prime factorization would be: 2 x 3 x 52.
The least common multiple (LCM) of two numbers is the smallest number (not zero) that is a multiple of both.
Toget it, first we have to get the prime factorization of each number and write all the prime factors with the highest exponent.
Example:
For numbers 72 and 150

Prime factorization of 72: : 23 x 32.Prime Factorization of 150: 2 x 3 x 52.
LCM: 23 x 32 x 52
The greatest common factor, or GCF, is the greatest factor that divides two numbers. To find the GCF of two numbers.
To get it, first...