But 276 mod 24 = 12, so instead compute: - Nelissen Grade advocaten

Understanding But 276 Mod 24 = 12: A Simple Guide to Modular Arithmetic You Can Compute Easily

When working with numbers, modular arithmetic is a powerful and intuitive tool—especially when dealing with remainders. A clean and often surprising fact in this area is:

> 276 mod 24 = 12, and instead of calculating long divisions, you can compute it quickly using basic math.

Understanding the Context

Let’s break down what this means, why it works, and how to apply it easily—perfect for students, programmers, or anyone curious about math simplifications.

What Does “276 mod 24 = 12” Really Mean?

The expression 276 mod 24 asks: “What’s the remainder when 276 is divided by 24?”
The result, 12, means 276 is 12 more than a multiple of 24.

But 276 mod 24 = 12, so instead compute:

Key Insights

Think of multiples of 24:
24 × 10 = 240
24 × 11 = 264
24 × 11.5 ≈ 276, but 24 × 12 = 288, so 276 is between 11 and 12 times 24.

Now compute:
276 – 264 = 12

So, indeed:
276 mod 24 = 12

Why Compute Quick Instead of Dividing?

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Final Thoughts

Instead of performing a full division, especially by hand, we can use:

Subtracting multiples of 24 from 276
Using known modular benchmarks (like multiples of 24)

This method is efficient and avoids complex division steps.

Step-by-Step: Compute 276 mod 24 Yourself

Goal: Find remainder when 276 is divided by 24, without long division.

Step 1: Find nearest lower multiple of 24

We know:
24 × 10 = 240
24 × 11 = 264
24 × 12 = 288 (too big)

So the largest multiple ≤ 276 is 264 (which is 24 × 11)

Step 2: Subtract and find the remainder

276 – 264 = 12

✅ Result:
276 mod 24 = 12