4. Tests of Divisibility
4. Tests of Divisibility
Embedded Files
Demonstrate proficiency in identifying tests of divisibility.
Applying tests of divisibility to solve problems.
A divisibility test is an easy way to identify whether the given number is divided by a fixed divisor without actually performing the division process.
These rules let you test if one number is divisible by another, without having to do too much calculation!
Example 1: Using tests of divisibility, check whether the following numbers are divisible by 2, 3, 4 and 6
a. 572
i) A number is divisible by 2 if the one's digit is 0, 2, 4, 6, 8. Here, the one’s digit in the number 572 is 2. Hence, the number is divisible by 2.
ii) A number is divisible by 3 if the sum of all the digits is divisible by 3.
572 = 5+7+2 = 14 ÷ 3) Since 14 is not divisible by 3, the number is not divisible by 3.
iii) A number is divisible 4 if the last two digits are divisible by 4. Here, the last two digits of the number 572 is 72. Since 72÷ 4 = 18, the number 572 is divisible by 4.
iv) A number is divisible by 6 if the number is divisible by both 2 and 3.
The number 572 is divisible by 2 but not divisible by 3. Hence, the number is not divisible by 6.
b. 72633
i) A number is divisible by 2 if the one's digit is 0, 2, 4, 6, 8. Here, the one’s digit in the number 72633 is 3. Hence, the number is not divisible by 2.
ii) A number is divisible by 3 if the sum of all the digits is divisible by 3.
72633 = 7+2+6+3+3 = 21. Since 21÷3 = 7, the number is divisible by 3.
iii) A number is divisible 4 if the last two digits are divisible by 4. Here, the last two digits of the number 72633 is 33. Since 33 is not divisible by 4, the number is not divisible by 4.
iv) A number is divisible by 6 if the number is divisible by both 2 and 3.
The number 72633 is not divisible by 2 and divisible by 3. Hence, the number is not divisible by 6.
Example 2: Tick (✓) the boxes if the number is divisible by the numbers on the top. Cross out (x) is the number is not divisible.
Watch a video to understand this better.
Vid 4.1 Rules of Divisibility
Summary :-
A divisibility test is an easy way to identify whether the given number is divided by a fixed divisor without actually performing the division process.
Extension
Relation of HCF and LCM:
LCM and HCF are the two important methods in Maths. The LCM is used to find the least possible common multiples of two or more numbers whereas HCF is a method to find the highest possible common factor among the numbers. But both can be related by the formulae:
LCM(a,b) = a × b / HCF(a,b)
HCF(a,b) = a × b / LCM(a,b)
Where a and b are the two numbers.
Watch a video to understand this better.
Vid 4.2 Relation Between HCF, LCM & Given Numbers
Page updated
Report abuse