Numbers Concepts

Factor

A number that divides into another number with no remainder

Eg. 12 = 1, 2, 3, 4, 6, 12

If you divide 12 by any of these numbers, it would be 0

Multiple

A number formed by multiplying that number by any natural number

Eg. If you multiply 3 by the numbers 1, 2, 3, 4 and so forth you get:

3 × 1 = 3

3 × 2 = 6

3 × 3 = 9

3 × 4 = 12

Prime Number

A natural number that only has 2 factors (1 and itself)

Eg. 11 only has 2 factors. 1 and 11.

Some of these numbers are:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29

Composite Numbers

A natural number that has more than 2 factors.

Eg. 12 has more than 2 factors. 1, 2, 3, 4, 5, 12

The fundamental theorem of arithmetic

It states that every composite number can be expressed as the product of prime number

Eg. 12 can be expressed as

2 × 2 × 3

or

2² x 3

Highest common factor (HCF)

The factor between two or more numbers that is the largest shared factor of all of the numbers

Lowest common multiple (LCM)

The multiple between two or more numbers that is the smallest shared multiple of all of the numbers

The product of two numbers

Equal to the HCF and LCM of these numbers