Divisibility Rule of 210

The divisibility rule for 210 is a method by which we can find out if a number is divisible by 210 or not without using the division method. A number is divisible by 210 if it is divisible by 2, 3, 5, and 7.

Example: Check whether 2310 is divisible by 210 using the divisibility rule.

Step 1: Check divisibility by 2. A number is divisible by 2 if it ends in an even digit. 2310 ends in 0, which is even, so it is divisible by 2.

Step 2: Check divisibility by 3. A number is divisible by 3 if the sum of its digits is divisible by 3. 2 + 3 + 1 + 0 = 6, which is divisible by 3, so 2310 is divisible by 3.

Step 3: Check divisibility by 5. A number is divisible by 5 if it ends in 0 or 5. 2310 ends in 0, so it is divisible by 5.

Step 4: Check divisibility by 7. Use the divisibility rule for 7: Double the last digit and subtract it from the rest of the number. If the result is divisible by 7, the original number is as well. 2310: Double 0 to get 0, subtract from 231 to get 231. Double 1 to get 2, subtract from 23 to get 21, which is divisible by 7.

Since 2310 is divisible by all these numbers, it is divisible by 210.
 

Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 210.

Know the multiples of 210:

Memorize the multiples of 210 (210, 420, 630, 840, 1050, etc.) to quickly check divisibility. If a number is a multiple of 210, it is divisible by 210.

Verify with smaller rules:

Check divisibility by 2, 3, 5, and 7 separately to ensure the number is divisible by 210.

Repeat the process for large numbers:

For large numbers, apply the divisibility rules repeatedly until you reach smaller numbers.

Example: Check if 44100 is divisible by 210 using the divisibility test.

- Divisible by 2: Ends in 0, so yes.
- Divisible by 3: Sum of digits 4 + 4 + 1 + 0 + 0 = 9, which is divisible by 3, so yes.
- Divisible by 5: Ends in 0, so yes.
- Divisible by 7: Double 0 to get 0, subtract from 441 to get 441. Double 1 to get 2, subtract from 44 to get 42, which is divisible by 7, so yes.

Since all conditions are met, 44100 is divisible by 210.

Use the division method to verify:

Use division to crosscheck results. This will help verify and also reinforce learning.
 

• Divisibility rule: The set of rules used to find out whether a number is divisible by another number or not.

• Multiples: Results obtained by multiplying a number by an integer. For example, multiples of 210 are 210, 420, 630, etc.

• Integers: Numbers that include all whole numbers, negative numbers, and zero.

• Subtraction: A process of finding the difference between two numbers by reducing one number from another.

• Even number: A number divisible by 2, such as 0, 2, 4, 6, 8, etc.