# Short Trick for Multiplying A Number by 21, 31, 41, 51, 61, 71, 81, 91, 101, 111, ...

**Tricks to Multiply any number by 21**

Let us understand how it works by multiplying **63852 X 21**

**Step 1: **Start by adding an imaginary 0(zero) after the number **638520**

**Step 2:** Multiply the rightmost number with 2, here in case is an imaginary number i.e.

0 X 2 = 0 and add with the corresponding number from left i.e. 0 + 2 = 2.

**Step 3:** Take one by one numbers from left and repeat step 2 i.e. 2 X 2 = 4 and add with the corresponding number from left i.e. 4 + 5 = 9 and place the number to the left number obtained in previous step i.e. 92

**Step 4:** Take one by one numbers from left and repeat step 2 i.e. 5 X 2 = 10 and add with the corresponding number from left i.e. 10 + 8 = 18 and place the number to the left number obtained in previous step i.e. 892 and keep the carry 1 for the next step.

**Step 5:** Take one by one numbers from left and repeat step 2 i.e. 8 X 2 = 16 and add with the corresponding number from left i.e. 16 + 3 = 19 and add it with the carry from the previous step i.e. 19 + 1 = 20 and place the number to the left number obtained in previous step i.e. 0892 and keep the carry 2 for the next step.

**Step 6: **Take one by one numbers from left and repeat step 2 i.e. 3 X 2 = 6 and add with the corresponding number from left i.e. 6 + 6 = 12 and add it with the carry from the previous step i.e. 12 + 2 = 14 and place the number to the left number obtained in previous step i.e. 40892 and keep the carry 1 for the next step.

**Step 7: **Take one by one numbers from left and repeat step 2 i.e. 6 X 2 = 12 and add it with the carry from the previous step i.e. 12 + 1 = 13 and place the number to the left number obtained in previous step i.e. 1340892.

So, 63852 X 21 = **1340892 (Answer)**

You may have noticed that the above example was with multiplication of 21. This method is applicable for any multiplication with number whose unit digit is 1 i.e. 21, 31, 41, 51……. Here’s an example to demonstrate.

**Tricks to Multiply any number by 31**

Let us understand how it works by multiplying **63852 X 31**

**Step 1:** Start by adding an imaginary 0(zero) after the number **638520**

**Step 2:** Multiply the rightmost number with 3, here in case is an imaginary number i.e. 0 X 3 = 0 and add with the corresponding number from left i.e. 0 + 2 = 2.

**Step 3:** Take one by one numbers from left and repeat step 2 i.e. 2 X 3 = 6 and add with the corresponding number from left i.e. 6 + 5 = 11 and place the number to the left number obtained in previous step i.e. 12 and keep the carry 1 for the next step.

**Step 4:** Take one by one numbers from left and repeat step 2 i.e. 5 X 3 = 15 and add with the corresponding number from left i.e. 15 + 8 = 23 add it with the carry from the previous step i.e. 23 + 1 = 24 and place the number to the left number obtained in previous step i.e. 412 and keep the carry 2 for the next step.

**Step 5:** Take one by one numbers from left and repeat step 2 i.e. 8 X 3 = 24 and add with the corresponding number from left i.e. 24 + 3 = 27 and add it with the carry from the previous step i.e. 27 + 2 = 29 and place the number to the left number obtained in previous step i.e. 9412 and keep the carry 2 for the next step.

**Step 6:** Take one by one numbers from left and repeat step 2 i.e. 3 X 3 = 9 and add with the corresponding number from left i.e. 9 + 6 = 15 and add it with the carry from the previous step i.e. 15 + 2 = 17 and place the number to the left number obtained in previous step i.e. 79412 and keep the carry 1 for the next step.

**Step 7:** Take one by one numbers from left and repeat step 2 i.e. 6 X 3 = 18 and add it with the carry from the previous step i.e. 18 + 1 = 19 and place the number to the left number obtained in previous step i.e. 1979412.

So, 63852 X 21 = **1979412 (Answer)**

Similarly, using this method you can calculate the product of any number when divided by number whose ones is 1 i.e 21, 31, 41, 51, 61, ...