Multiples and Factors

Home / Number Theory / Multiples and Factors

By Math Original No comments
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.

 

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 (M4).

M4 = 4, 8, 12, 16, 20, 24, 28, 32

List several multiples of 6 (M6).

M6 = 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.

 

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.

F16 = 1, 2, 4, 8, 16

F24 = 1, 2, 4, 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 1, 3, 5, 15. Our number can be divisible by each of this numbers without having a reminder.

See more about prime numbers here

 

 

 

New Exercises & LecturesDon't lose new posts and lectures from MathOriginal.