divisors factors and multiples
TRANSCRIPT
DIVISORSDIVISORS
How many divisors does a number have?
Suppose you wish to find the number of divisors of 48. Starting with 1 we can work through the set of natural numbers and test divisibility in each case, noting that divisors
can be listed in factor pairs.
48 = 1×48 = 2×24 = 3×16 = 4×12 = 6×8
44
As we can see, 6 can be written as product of two numbers in many ways: 6 = 1 × 6
6 = 2 × 3
6 = 3 × 2
6 = 6 × 1
1, 2, 3 and 6 are exact divisors of 6
MULTIPLESThe products of a number with the natural numbers 1,2,3,4,5, …. Are called MULTIPLES of a number.
For example:7x1=7 7x2=14
7x5=35So the multiples of 7 are 7, 14 and 35 and so on.
The multiples of a number are obtained by multiplying the number by each of the natural numbers.
For example:multiples of 4 are 4, 8, 12, 16, …
6
Multiples of 2 = 2,4,6,8,10,12,14,16,18,20,22,24…
Multiples of 3 = 3,6,9,12,15,18,21,24,27,30,33,36,…
Multiples of 15 = 15,30,4,60,75,90,105,120,135,……
The number of multiples of a given number is infinite.
FACTOR
A factor of a number is an exact
divisor of that number i.e. the factor
leaves remainder 0 when it divides
the number.
4 × 5 = 20
4 and 5 are factors of 20. We can also say that 20 is multiple of 4 and 5.
In 2 × 12 = 24,
2 and 12 are factors of 24.
24 is the multiple of 2 and 12.
So, a number is a multiple of its factors.
POINTS TO REMEMBER
• 1 is a factor of every number.
• Every factor of a number is an exact divisor of that number.
• Every factor is less than or equal to the given number.
• Number of factors of a given number are finite.
• Every multiple of a number is greater than or equal to that number.
• The number of multiples of a given number is infinite.
• Every number is a multiple of itself.
POINTS TO REMEMBER