Trick to Multiply 4 Digits by 4 Digits

Last Updated : 21 Aug, 2025

Are you looking to speed up your 4-digit by 4-digit multiplication without relying solely on traditional methods? Whether you're a student aiming to improve your mental math or a teacher searching for innovative ways to simplify complex multiplication, learning these quick multiplication tricks can be a game-changer.

In this article, we’ll explore proven strategies—such as the Box/Window method, lattice multiplication, and breaking numbers into partial products—that make multiplying large numbers fast and intuitive.

Trick to Multiply 4 Digits by 4 Digits

There are some tricks to multiply large number such as 4 digit number i.e.,

  • Break It Down Using Place Value
  • Distributive Property
  • Vedic Math Method (Vertical and Crosswise)

Break It Down Using Place Value

One of the most effective ways to simplify 4-digit multiplication is by breaking the numbers down into smaller parts, using their place values.

For example, if you are multiplying 1234 × 5678, you can think of it like this:

1234 × 5678 = (1000 + 200 + 30 + 4) × 5678

Now, multiply each part of 1234 by 5678:

1000 × 5678 = 5678000

200 × 5678 = 1135600

30 × 5678 = 170340

4 × 5678 = 22712

Finally, add up all these parts: 5678000 + 1135600 + 170340 + 22712 = 7005652

1234 × 5678 = 7005652

By breaking the multiplication into smaller steps, you can handle it in manageable chunks.

Use the Distributive Property

The distributive property is a key mathematical principle that allows you to break down larger problems into smaller, easier parts. This can be applied to multiplication by expanding one of the numbers.

For instance, using the example 4567 × 1234, you can distribute 1234 as follows:

4567 × 1234 = 4567 × (1000 + 200 + 30 + 4)

Now, solve each part step-by-step:

4567 × 1000 = 4567000

4567 × 200 = 913400

4567 × 30 = 137010

4567 × 4 = 18268

Add them together to get the final result: 4567000 + 913400 + 137010 + 18268 = 5634678

This method keeps the multiplication steps manageable.

Vedic Math Method

Let’s say you are multiplying two numbers: ABCD × WXYZ

  • Multiply D × Z (Units place of both numbers)
    • Write down the result. This is the last digit of the final answer.
  • Cross multiply the last two digits and add:
    • Multiply C × Z and D × Y, and add them. Carry over if needed.
  • Cross multiply the last three digits and add:
    • Multiply B × Z, C × Y, and D × X, then add them together. Carry over as needed.
  • Multiply all four digits in a crosswise fashion:
    • Multiply A × Z, B × Y, C × X, and D × W. Sum them up and handle the carryover.
  • Reverse the process for the next digits:
    • Now go backward with cross products (A × Y, B × X, etc.).
  • Finish with the first digits (A × W).
    • Sum up all the results, including carrying over the values as needed to get the final answer.

For ABCD × WXYZ, we can visualize this as follows:

Trick-to-Multiply-4-Digits-by-4-Digits-02

Now let us see one example 5243 × 7326

Step 1: (d × h) = 3 × 6= 18. Take "8" for answer and “1” to be carry over to next step (Ans: 8)

Step 2: [ (c × h) + (d × g)] + add number if any carry over from previous step

i.e. [(4 × 6) + (3 × 2)] + 1 = 31. Take "1" for answer and “3” to be carry over to next step (Ans: 18)

Step 3: [ (b × h) + (c × g) + (d × f)] + add number if any carry over from previous step

i.e. [(2 × 6) + (4 × 2) + (3 × 3)] + 3 = 32. Take "2" for answer and “3” to be carry over to next step (Ans: 218)

Step 4: [(a × h) + (b × g) + (c × f) + (d × e)] + add number if any carry over from previous step.

i.e. [(5 × 6) + (2 × 2) + (4 × 3) + (3 × 7)] + 3 = 70. Take "0" for answer and “7” to be carry over to next step (Ans: 0218)

Step 5: [(a × g) + (b × f) + (c × e)] + add number if any carry over from previous step

i.e. [(5 × 2) + (2 × 3) + (4 × 7)] + 7 = 51. Take "1" for answer and “5” to be carry over to next step (Ans: 10218)

Step 6: [ (a × f) + (b × e)] + add number if any carry over from previous step

i.e. [(5 × 3) + (2 × 7)] + 5 = 34. Take "4" for answer and “3” to be carry over to next step (Ans: 410218).

Step 7: (a × e) + add number if any carry over from previous step

i.e. (5 × 7) + 3 = 38 (Ans: 38410218)

So final answer is 38410218.

Solved Examples on 4 Digit Multiplication by 4 Digit Trick

Example 1: Multiply 2345 and 6789.

Solution:

2345 × 6789 = (2000 + 300 + 40 + 5) × 6789

Calculating each part:

2000 × 6789 = 13578000

300 × 6789 = 2036700

40 × 6789 = 271560

5 × 6789 = 33945

Adding them together:

13578000 + 2036700 + 271560 + 33945 = 15905205

Final Result: 15905205

Example 2: 4567 × 1234

Solution:

4567 × 1234 =4567 × (1000 + 200 + 30 + 4)

Calculating each part:

4567 × 1000 = 4567000

4567 × 200 = 913400

4567 × 30 = 137010

4567 × 4 = 18268

Adding them together:

4567000 + 913400 + 137010 + 18268 = 5634678

Final Result: 4567 × 1234 = 5634678

Example 3: Multiply 5243 and 7326.

Solution:

3 × 6 = 18 (Take 8, carry 1)

(4 × 6) + (3 × 2) + 1 = 31 (Take 1, carry 3)

(2 × 6) + (4 × 2) + (3 × 3) + 3 = 32 (Take 2, carry 3)

(5 × 6) + (2 × 2) + (4 × 3) + (3 × 7) + 3 = 70 (Take 0, carry 7)

(5 × 2) + (2 × 3) + (4 × 7) + 7 = 51 (Take 1, carry 5)

(5 × 3) + (2 × 7) + 5 = 34 (Take 4, carry 3)

(5 × 7) + 3 = 38

Combining the results:

38410218

Final Result: 5243 × 7326 = 38410218

Example 4: 3124 × 5678

Solution:

3124 × 5678 = (3000 + 100 + 20 + 4) × 5678

Calculating each part:

3000 × 5678 = 17034000

100 × 5678 = 567800

20 × 5678 = 113560

4 × 5678 = 22712

Adding them together:

17034000 + 567800 + 113560 + 22712 = 17777712

Final Result: 3124 × 5678 = 17777712

Example 5: Multiply 6421 and 3547.

Solution:

1 × 7=7 (Take 7, carry 0)

(2 × 7) + (1 × 4) + 0 = 14 (Take 4, carry 1)

(4 × 7) + (2 × 4) + (1 × 5) + 1 = 41 (Take 1, carry 4)

(6 × 7) + (4 × 4) + (2 × 5) + (1 × 3) + 4 = 63 (Take 3, carry 6)

(6 × 3) + (4 × 5) + (2 × 4) + 6 = 56 (Take 6, carry 5)

(6 × 5) + 5 = 30 (Take 0, carry 3)

(6 × 3) + 3 = 21

Combining the results: 22763507

Final Result: 6421 × 3547 = 22763507

Practice Questions on 4-digit Multiplication by 4-digit Tricks

Q1. 1256 × 7890

Q2. 4321 × 5678

Q3. 3142 × 1589

Q4. 2765 × 3492

Q5. 4873 × 2154

Q6. 2398 × 7426

Q7. 3584 × 6210

Answer Key

  1. 9,906,840
  2. 24,514,838
  3. 4,990,138
  4. 9,650,580
  5. 10,497,342
  6. 17,797,348
  7. 22,260,640

Conclusion

In conclusion, mastering the trick to multiply 4-digit numbers quickly can save time and make complex calculations easier. By breaking down the numbers into smaller parts and using methods like the distributive property or shortcuts like vertical and crosswise multiplication, you can simplify what seems like a daunting task.

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