you have 3 sisters. your mother asked me to divide 45645 toffees among them equally. using the test of divisibility find out if you can divide equally. give reasons.
Answers
Step-by-step explanation:
Divisibility Rules
Divisibility Test by 2
If the ones digit or unit’s place digit of a number is either 0, 2, 4, 6 0r 8 then the number is said to be divisible by 2. In other terms, if the last digit of the number is even then it is always divisible by 2. For example, let’s take 24. The last digit is even. 4 is divisible by 2, so the number is divisible by 2.
Divisibility Test by 4
A number is divisible by 4 if the number formed by the last two digits is divisible by 4. For example, let’s take 12343684. You don’t need to worry about all the numbers, just check the last 2 digits of the numbers. If the last two digits i.e 84 are divisible by 4than the number is divisible by 4.
Divisibility Test by 3 and 9
A number is divisible by 3 if the sum of its digits is divisible by 3. Let’s have a look at some examples.
121: Here the sum of the digit is 4. Is 4=the number 4 divisible by 3? No.
123: Here the sum of the digit is 6 and yes 6 is divisible by 3. So the number 123 is divisible by 3.
Same rules are applied to the divisibility test of 9. A number is divisible by 9 if the sum of its digits is divisible by 9.
Test of Divisibility by 5
A number is exactly divisible by 5 if it has the digits 0 or 5 at one’s place. The numbers like 15,120,205,4400 etc. are exactly divisible by 5 as these numbers have 0 or 5 in the one’s place. Let’s look at an example.
In the numbers 21345650 and 459022, which one is exactly divisible by 5? Out of both the numbers 21345650 and 459022, the first number i.e 21345650 is exactly divisible by 5 as the ones place is occupied by 0.
Test of Divisibility by 6
A number is exactly divisible by 6 if that number is divisible by 2 and 3 both. For checking the divisibility of the number with 6 we have to apply the rule of divisibility tests that we apply for numbers 2 and 3. Let’s look at an example. Using the divisibility tests rule for 6, check whether the following number is divisible by 6: 12,581.
In the number 12,581 the ones digit does not have any of the numbers like 0,2,4,6,8 in the ones place. So the number is not divisible by 2. Hence the number is not divisible by 6 because for a number to be divisible by 6, it has to be divisible by 2 and 3 both.
Test of Divisibility by 8
The test of divisibility by 8 is used in numbers with four or more digits. A number is exactly divisible by 8 if the number formed by the digits in ones, tens and hundredth place is divisible by 8. In the number 5864, we see that the number formed by the digits in ones, tens and hundredth place, 864 which is divisible by 8, so the number is divisible by 8.
For example, whether the following number is divisible by 8: 5,87,824. In the numbers given above, the number 5,87,824 has 824 in the ones, tens and hundredth place. This number is exactly divisible by 8, hence the number is divisible by 8.
Answer:
A number is divisible by 3 if the sum of its digits is divisible by 3. A number is divisible by 9 if the sum of its digits is divisible by 9. And a number is divisible by 6 if it is divisible by 2 (even number) and by 3.