# Multiplication of a Number by a 3-Digit Number with Examples | How to Multiply by 3-digit Numbers?

Multiplication is one of the important topics that every student has to learn. It is one of the arithmetic operations. Students have to learn to multiply a number by 1 digit number, 2 digit number before learning this topic. Multiplication of a number by a 3 digit number means multiplicand will be a three-digit number irrespective of the multiplier. Find the detailed explanation of two simple methods to solve the multiplying a number by a 3 digit number in the further sections.

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## Multiplication of a Number by a 3-Digit Number

It means 3 digit number will the multiplicand and number is the multiplier. Get the simple tricks and techniques to find the product of a number by a 3-digit number in the below-mentioned sections.

Method 1: Column Method

• Write the multiplicand, multiplier in two different columns.
• At first, multiply the unit digit of the second number by the first number (the order of the digits is from left to the right)
• Write the product in the third column.
• Multiply the ten’s digit of the second number by the first number.
• Place x symbol at the unit’s place of the fourth column followed by the product of ten’s digit.
• Again, multiply the hundred’s digit of the bottom number by the top number.
• Place x symbols at the unit’s place, ten’s place of the fifth column and the product.
• Find the sum of the products to get the final result.

Method 2: Expansion Method

• Expand both numbers.
• Express the expansion in the place of original numbers.
• Use the distributive property for further expansion.
• Compute the product of each number and then add to get the product.

### Multiplying a Number by 3-Digit Number Examples

Question 1:
Solve 456 x 289 using the column method.
Solution:
Given that,
456 x 289

Multiply 9 by 456. 9 x 456 = 4104
Multiply 8 by 456. 8 x 456 = 3648
Multiply 2 by 456. 2 x 456 = 912
Place those products in the order mentioned above.
4104 + 36480 + 91200 = 131784.
So, 456 x 289 = 131784.

Question 2:
Solve 85 x 426 using the expansion method.
Solution:
Given that,
85 x 426
Expand the numbers
85 = 80 + 5
426 = 400 + 20 + 6
85 x 426 = (80 + 5) x (400 + 20 + 6)
Using the distributive property
= 80 x (400 + 20 + 6) + 5 x (400 + 20 + 6)
= (80 x 400) + (80 x 20) + (80 x 6) + (5 x 400) + (5 x 20) + (5 x 6)
= 32000 + 1600 + 480 + 2000 + 100 + 35
= 36210
Therefore, 85 x 426 = 36210.

Question 3:
Compute 1254 x 125
Solution:
Given that,
1254 x 125

Multiply 5 by 1254. 5 x 1254 = 6270
Multiply 2 by 1254. 2 x 1254 = 2508
Multiply 1 by 1254. 1 x 1254 = 1254
Place those products in the order mentioned above.
6270 + 25080 + 125400 = 156750
So, 1254 x 125 = 156750.

Question 4:
Find 7845 x 364
Solution:
Given that,
7845 x 364

364 = 300 + 60 + 4
7845 x 364 = 7845 x (300 + 60 + 4)
= 7845 x 300 + 7845 x 60 + 7845 x 4
= 2353500 + 470700 + 31380
= 2855580
Therefore, 7845 x 364 = 28,55,580

### FAQs on Multiplying by Three Digit Number

1. How do you multiply 3 digit numbers quickly?
We must use the column method to multiply the three-digit numbers quickly.

2. Use the expansion method and multiply 67 by 153?
67 x 153 = 67 x (100 + 50 + 3)
= 67 x 100 + 67 x 50 + 67 x 3
= 6700 + 3350 + 201
= 10251.

3. Why a 3 digit multiplication has 3 columns products?
Because in a three-digit multiplication the second number will be the 3 digit number. So, every 3 digit multiplication has 3 sub-products. By adding those sub-products, we get the final product.

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