Work Modulo a Prime
Add, multiply, and stay inside the mod.
Work Modulo a Prime is a free Coding Interview Prep lesson on CoddyKit — lesson 1 of 4. You can read the complete lesson below for free — then practise it hands-on in the browser with a built-in code editor and a 24/7 AI tutor. It is part of the Coding Interview Prep learning path, one of 4 lessons in the course, and your progress syncs across the web and the CoddyKit app.
Why Take the Modulo
Contest answers can grow huge, way past any integer type elsewhere. So problems ask for the result modulo a big prime to keep numbers small. 🔢
Meet the Famous Mod
The prime you will see most is 1000000007, often written 1e9+7. It is just big enough to dodge collisions and small enough to fit in 64 bits.
MOD = 1000000007What Modulo Means
The modulo operator gives the remainder after division. So 17 % 5 is 2, because 17 leaves a remainder of 2 when divided by 5.
print(17 % 5) # 2Addition Stays Inside
You can add first and take the mod at the end, or mod as you go. The remainder is the same either way, so reduce often to stay small.
total = (a + b) % MODMultiplication Stays Inside Too
The same rule holds for multiplication: take the product mod the prime. Python handles big ints natively, but modding keeps every value tiny and fast.
prod = (a * b) % MODReduce After Every Step
In a long loop, apply % MOD on every iteration. This stops numbers from ballooning and keeps each operation cheap and predictable.
ans = (ans * i) % MODSubtraction Can Go Negative
Subtraction may produce a negative remainder in many languages. Add MOD back before the final mod so the result lands in the safe 0 range.
diff = (a - b + MOD) % MODPython's Friendly Modulo
Good news: Python's % already returns a non-negative result for a positive modulus. So -1 % 7 gives 6, not -1, saving you a fix-up.
print(-1 % 7) # 6Mod Distributes Over Operations
The core idea: (a op b) % m equals (a%m op b%m) % m for add and multiply. That lets you reduce inputs before combining them.
Division Is the Catch
Add, subtract, and multiply work cleanly under a mod. But plain division does not, and you will need a modular inverse for it later in this course.
Set MOD Once at the Top
Define MOD as a constant at the start of your solution. One named value beats scattering 1000000007 across the code where a typo can hide.
MOD = 10**9 + 7Quick Check
Why add MOD before taking the mod of a subtraction?
Recap
You now keep huge counts small with a prime modulus like 1e9+7. Reduce add, subtract, and multiply at every step, mind negatives, and save division for inverses. 🎯
Frequently asked questions
Is the “Work Modulo a Prime” lesson free?
Yes — the full text of “Work Modulo a Prime” is free to read here on the web, and the Coding Interview Prep course includes 4 lessons in total. To practise it interactively (a built-in code editor and a 24/7 AI tutor) and unlock the rest of the Coding Interview Prep course, upgrade to CoddyKit PRO.
What will I learn in “Work Modulo a Prime”?
Add, multiply, and stay inside the mod. You practise Coding Interview Prep with hands-on code you run directly in the browser, and a 24/7 AI tutor answers your questions as you work through the lesson.
Do I need any experience to start Coding Interview Prep?
No prior experience is required. Coding Interview Prep on CoddyKit is structured for beginners through advanced learners; this is — lesson 1 of 4, so you can start here or from the beginning and move at your own pace.
How long does the “Work Modulo a Prime” lesson take?
Most CoddyKit lessons take about 5–10 minutes. Each one is bite-sized and interactive, so you make steady progress and pick up exactly where you left off across the web and the app.
Can I write and run code in this Coding Interview Prep lesson?
Yes. Every Coding Interview Prep lesson includes a built-in code editor, so you write and run real code right in your browser and get instant AI feedback — no local setup required.