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## Multiples

You can think multiples of a number as the” times table” for that number. For example: the multiplies of 3 are:
3 × 1 = 3,  3 × 2 = 6,  3 × 3 = 9 and so on.

A multiple of a number is found when you multiply that number by a positive integer. The first multiply of any number is the number itself (the number multiplied by one).

**INTEGER** Any of the negative and the positive whole numbers including zero.

Worked example 1

a) Which are the first 5 multiples of 7?

b) Is 280 a multiple of 4?

c) Is 363 a multiple of 5?

Solution

a) To find these, multiply 7 by 1, 2, 3, 4 and 5.

7 x 1 = 7

7 x 2 = 14

7 x 3 = 21

7 x 4 = 28

7 x 5 = 35

Answer: The first 5 multiples of 7 are: 7, 14, 21, 28, 35.

b) To find out divide 280 by 4. If it goes exactly, then 280 is a multiple of 4.

280 : 4 = 70.

Answer: 280 is a multiple of 4.

c) To find out divide 363 by 5. If it goes exactly, then 2363 is a multiple of 5.

363 : 5 = 70, reminder 13.

Answer: No, 363 isn’t a multiple of 5.

## The lowest common multiplies of two or more numbers is the smallest number that is multiple of all given numbers.

### To find LCM read the articleLCM and HCF

Worked example 2: Find the lowest common multiple of 4 and 6.

Solution: List several multiples of 4 (M4).

M= 4, 8, 12, 16, 20, 24, 28, 32

List several multiples of 6 (M6).

M= 6, 12, 18, 24, 30, 36, 42

Find the lowest number that appears in both sets. This is LCM

## Factors

A factor is a number that divides exactly into another number with no reminder. For example, 3 is a factor of 24 because it goes into 24 exactly 8 times. The number 1 is a factor of every number.  The largest factor of any number is the number itself.

### The highest common factor (HCF)

The highest common factor of two or more numbers is the highest number that is a factor of all the given numbers.

### To find HCF read the articleLCM and HCF

Worked example 3:Find the HCF of 16 and 24

Solution:List the factors of each number and underline the factors that appear on both sets.

F16 = 1, 248, 16

F24 = 1, 24, 6, 8, 12, 24

Pick out the highest underlined factor.

Answer: HCF = 8

### Prime and Composite numbers

Prime numbers are numbers that have exactly two factors: one and the number itself.

5 is an example of a prime number because it has exactly two factors. The number itself 5 and the number 1. So, it can’t be divisible by any other whole number without having a reminder.

Composite numbers are numbers that have more than two factors.

15 is an example of a composite number because it has more than two factors. The factors are 13515. Our number can be divisible by each of this numbers without having a reminder.

See more about prime numbers here

Next article

### Prime and composite numbers

Prime numbers are numbers that have exactly two factors: one and the number itself.

Composite numbers are numbers that have more than two factors.

Next article

### Prime and composite numbers

Prime numbers are numbers that have exactly two factors: one and the number itself.

Composite numbers are numbers that have more than two factors.