Russian Peasant Multiplication: The Ancient Method That Uses Only Doubling and Halving

Multiplication is probably the most important elementary operation in mathematics. Every math enthusiast develops their own preferred techniques over time.

But have you ever multiplied two numbers using only doubling and halving? No multiplication tables required?

This method has been around for thousands of years. The ancient Egyptians used it. Russian peasants passed it down through generations (hence the name). And it’s still fascinating today because it reveals a deep connection between arithmetic and binary numbers.

Let me show you how it works.

The Method in Action: 48 × 35

Let’s multiply 48 by 35 using this technique.

Step 1: Set Up Two Columns

Write your two numbers in separate columns, side by side.

Put 48 in the left column and 35 in the right column. (It doesn’t actually matter which number goes where – the result is the same.)

Step 2: Double the Left, Halve the Right

Now comes the core operation:

• Left column: Keep doubling (multiply by 2)
• Right column: Keep halving (divide by 2, dropping any remainder)

Continue until the right column reaches 1.

Here’s what happens:

Left (×2)	Right (÷2)
48	35
96	17
192	8
384	4
768	2
1536	1

Important: When halving odd numbers, drop the fraction. 35 ÷ 2 = 17.5 becomes just 17. We only work with whole numbers.

Step 3: Cross Out Rows Where Right Column is Even

Look at the right column. Any row where the right number is even gets crossed out entirely.

Left	Right	Keep?
48	35	✓ ODD
96	17	✓ ODD
192	8	✗ EVEN
384	4	✗ EVEN
768	2	✗ EVEN
1536	1	✓ ODD

Notice that the last row (where right = 1) is always kept, since 1 is odd.

Step 4: Sum the Remaining Left Column Numbers

Add up all the left-column numbers that weren’t crossed out.

48 + 96 + 1536 = 1680

And there’s your answer: 48 × 35 = 1680 ✓

The Complete Process at a Glance

Here’s the entire method visualized in one diagram:

Why Does This Actually Work?

This isn’t magic – it’s binary arithmetic in disguise.

When you halve numbers and check if they’re odd or even, you’re essentially reading the binary representation of that number. Each “odd” row corresponds to a 1 in the binary representation; each “even” row corresponds to a 0.

Let’s break it down:

35 in binary = 100011

This means: 35 = 32 + 2 + 1 = 2⁵ + 2¹ + 2⁰

So when we multiply 48 × 35, we’re really computing:

• 48 × 32 = 1536 (row 6, right column = 1, which is odd)
• 48 × 2 = 96 (row 2, right column = 17, which is odd)
• 48 × 1 = 48 (row 1, right column = 35, which is odd)

Total: 1536 + 96 + 48 = 1680

The rows we kept correspond exactly to the powers of 2 that make up 35!

Another Example: 88 × 45

Let’s verify with another calculation.

Left (×2)	Right (÷2)	Keep?
88	45	✓ ODD
176	22	✗ EVEN
352	11	✓ ODD
704	5	✓ ODD
1408	2	✗ EVEN
2816	1	✓ ODD

Sum: 88 + 352 + 704 + 2816 = 3960

Check: 88 × 45 = 3960 ✓

When Would You Actually Use This?

I’ll be honest – you’re not going to use this for everyday calculations. It’s longer than standard multiplication once you know your times tables.

But this method is valuable for:

1. Teaching binary concepts – It makes binary numbers tangible
2. Computer science education – This is essentially how computers multiply
3. Historical appreciation – The Egyptians used this 4,000 years ago
4. Mental math party tricks – Impress friends by multiplying without knowing any multiplication facts beyond doubling
5. Backup method – If you only know how to double and halve, you can multiply anything

Try It Yourself

Practice with these:

1. 23 × 17 = ?
2. 56 × 43 = ?
3. 127 × 89 = ?

Work through the table, cross out even rows, sum what remains.

The Beauty of Ancient Mathematics

What amazes me about this method is that ancient Egyptians discovered an algorithm that modern computers essentially still use. They didn’t know about binary numbers or computer science – they just found a pattern that worked.

The fact that doubling, halving, and checking for odd/even naturally decomposes into binary multiplication is one of those beautiful coincidences in mathematics that feels almost inevitable in hindsight.

Try it a few times. Once you see the pattern, you’ll never forget it.