We know to multiply two digit numbers by twodigit numbers, and threedigit numbers by onedigit or twodigit numbers.
Now, we will learn the multiplication by threedigit numbers.
In multiplication of a number by a 3digit number are explained here step by step.
Consider the following examples on multiplication of a number by a 3digit number:
I. Examples to multiply 2digit numbers by a 3digit numbers:
1. Find the product of 36 × 137
Solution:
(i) First Method
(ii) Second Method
(a) 137 = 7 ones + 3 tens + 1 hundred 
II. Examples to multiply 3digit numbers by a 3digit numbers:
2. Multiply 543 by 278
Solution:
(i) First Method
(a) 278 = 8 + 70 + 200 
(ii) Second Method
(a) 278 = 8 ones + 7 T + 2 H 
3. Multiply 827 × 107
Solution:
Answer: 88489
4. Multiply 474 × 240
Solution:
Answer: 113760
Multiplying by 3Digit Number
5. Find the product of 528 and 378.
Step I: Arrange the numbers vertically. Step II: Multiply 528 by 8 528 × 8 = 4224 Step III: Multiply 528 by 70 528 × 70 = 36960 Step IV: Multiply 528 by 300 528 × 300 = 158400 Step V: Add: 4224, 36960 and 158400 4224 + 36960 + 158400 = 199584 
Hence, 528 × 378 = 199584 
6. Multiply 345 by 224.
The product is 77,280. 
Step I: Multiply 345 by 4 ones. 345 × 4 = 1380 ones = 1380 Step II: Multiply 345 by 2 tens. 345 × 2 = 690 tens = 6900 Step III: Multiply 345 by 2 hundreds. 345 × 2 = 690 hundreds = 69000 Step IV: Add the products. 
7. Multiply 625 by 124.
Solution: 124 = 100 + 20 + 4 We multiply 625 by 4, 20 and 100 respectively. Finally, we add the results to get the required product. 
Therefore, the product of 625 and 124 = 77,500.
III. Example to multiply 4digit numbers by a 3digit numbers:
8. Multiply 2437 by 324
Solution:
(i) First Method
The product = 789588
(ii) Second Method
(a) 324 = 4 ones + 2 tens + 3 hundreds 
These are the examples discussed on multiplication of a 2digit, 3digit and 4digit number by a 3digit number.
9. Multiply 2345 by 142.
The product is 3,32,990. 
Step I: Multiply 2345 by 2 ones. 2345 × 2 = 4690 ones = 4690 Step II: Multiply 2345 by 4 tens. 2345 × 4 = 9380 tens = 93800 Step III: Multiply 2345 by 1 hundred. 2345 × 1 = 2345 hundreds = 234500 Step IV: Add the products. 
10. Multiply 1519 and 402.
Solution: 402 = 400 + 0 + 2 We multiply 1519 by 2, 0 and 400 respectively. Finally, we add the results to get the required product. 
The product is 6,10,638.
11. Find the product of 2129 and 426.
426 = 400 + 20 + 6
We multiply 2129 by 6, 20 and 400 respectively.
Finally, we add the results to get the required product.
Therefore, 2129 × 426 = 9,06,954
Worksheet on Multiplication of a Number by a 3Digit Number:
1. Multiply the given 3digit numbers by a 3digit numbers by column method.
(i) 137 × 112 = __________
(ii) 258 × 135 = __________
(iii) 429 × 283 = __________
(iv) 647 × 465 = __________
(v) 874 × 509 = __________
(vi) 173 × 194 = __________
Answers:
(i) 15344
(ii) 34830
(iii) 121407
(iv) 300855
(v) 444866
(vi) 33562
2. Multiply 3digit by 3digit numbers:
(i) 354 by 435
(ii) 508 by 434
(iii) 458 by 392
(iv) 601 by 124
Answer:
2. (i) 153990
(ii) 220472
(iii) 179536
(iv) 74524
3. Find the following products:
(i) 
H 
T 
O 
(ii) 
H 
T 
O  
8 
5 
4 
8 
1 
6  
× 
2 
5 
4 
× 
6 
3 
4 












(iii) 
H 
T 
O 
(iv) 
H 
T 
O  
3 
5 
1 
6 
2 
1  
× 
2 
5 
3 
× 
1 
3 
6 












Answer:
3. (i) 216916
(ii) 517344
(iii) 88803
(iv) 84456
4. Multiply the given 4digit numbers by a 3digit numbers by column method.
(i) 1392 × 271 = __________
(ii) 2058 × 380 = __________
(iii) 5483 × 126 = __________
(iv) 4021 × 108 = __________
(v) 3281 × 288 = __________
(vi) 3016 × 160 = __________
Answers:
4. (i) 377232
(ii) 782040
(iii) 690858
(iv) 434268
(v) 944928
(vi) 482560
5. Multiply the following.
(i) 5424 × 8
(ii) 58549 × 128
(iii) 456 × 729
(iv) 639 × 199
(v) 5024 × 632
(vi) 76592 × 8
Answer:
5. (i) 43392
(ii) 7494272
(iii) 332424
(iv) 127161
(v) 3175168
(vi) 612736
6. Multiply 4digit by 3digit numbers:
(v) 4,032 by 196
(vi) 5,012 by 132
(vii) 5,647 by 243
(viii) 3,012 by 213
Answer:
6. (v) 790272
(vi) 661584
(vii) 1372221
(viii) 641556
7. Find the following products:
(i) 
Th 
H 
T 
O 
(ii) 
Th 
H 
T 
O 
5 
2 
5 
6 
4 
0 
2 
6  
× 
2 
6 
7 
× 
2 
4 
5 












(iii) 
Th 
H 
T 
O 
(iv) 
Th 
H 
T 
O 
2 
3 
6 
8 
6 
3 
2 
8  
× 
3 
9 
1 
× 
1 
5 
4 












(v) 
Th 
H 
T 
O 
(vi) 
Th 
H 
T 
O 
3 
8 
8 
4 
1 
9 
2 
4  
× 
2 
4 
3 
× 
3 
3 
0 


(vii) 
Th 
H 
T 
O 
(viii) 
Th 
H 
T 
O 
2 
0 
1 
8 
5 
3 
4 
2  
× 
1 
6 
4 
× 
1 
0 
3 










Answer:
7. (i) 1403352
(ii) 986370
(iii) 925888
(iv) 974512
(v) 943812
(vi) 634920
(vii) 330952
(viii) 550226
Related Concept
● Addition
● Check for Subtraction and Addition
● Word Problems Involving Addition and Subtraction
● Estimating Sums and Differences
● Multiply a Number by a 2Digit Number
● Multiplication of a Number by a 3Digit Number
● Word Problems on Multiplication
● Division of TwoDigit by a OneDigit Numbers
● Division of FourDigit by a OneDigit Numbers
● Division by 10 and 100 and 1000
● Division by TwoDigit Numbers
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