Multiples and factors note

Patterns in Numbers

Prime number – has only two factors or 1 x itself eg. 7 factors of 7 are 1 x 7 1, 7
Composite number -has more than two factors.

Factors
Please make sure you understand the following concepts:


GCF (Greatest Common Factor) (greatest meaning the biggest number in common between two or more numbers)
(The greatest common factor, or GCF, is also the greatest factor that divides two numbers.)

one way - You can list all of the factors and then rearrange them in a diagram.
Which numbers are common? Which number is the largest?

Or

Find the prime factors for the numbers.

14, 49 Solution: List the prime factors of each.14: 2 × 7 49: 7 × 7 7 is the only common factor; therefore, 7 is the GCF.
15, 75 Solution: List the prime factors of each.15: 3 × 5 75: 3 × 5 × 5 3 and 5 are common; therefore, 3 × 5 = 15 is the GCF.


Multiples

- LCM (Lowest Common Multiple) (lowest meaning the smallest number in common between two or more numbers)

One way - List all of the multiples eg. Like a times table chart.
multiples of 6 are 6, 12, 18, 24
And multiples of 8 are 8, 16, 24, 32….Find the lowest number that is common to both.

Or

Find the LCM of these sets of numbers.
3, 9, 21 List the prime factors of each.3: 3 9: 3 × 3 21: 3 × 7Multiply each factor the greatest number of times it occurs in any of the numbers.
9 has two 3s, and 21 has one 7, so we multiply 3 two times, and 7 once.
3 x 3 x 7 = 63
This gives us 63, the smallest number that can be divided evenly by 3, 9, and 21. We check our work by verifying that 63 can be divided evenly by 3, 9, and 21.