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**Multiples and Factors**

**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.

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**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 multiple (LCM)**

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 article **LCM and HCF**

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

**Solution: **List several multiples of 4 (M_{4}).

M_{4 }= 4, 8, **12**, 16, 20, 24, 28, 32

List several multiples of 6 (M_{6}).

M_{6 }= 6, **12**, 18, 24, 30, 36, 42

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

**Answer: LCM = 12**

**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.

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**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.

**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.

F_{16} = 1, __2__, __4__, ** 8**, 16

F_{24} = 1, __2__, __4__, 6, ** 8**, 12, 24

Pick out the highest underlined factor.

**Answer: HCF = 8**

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**Prime and composite numbers**

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**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 **1**, **3**, **5**, **15**. Our number can be divisible by each of this numbers without having a reminder.

See more about prime numbers **here**