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SSAT MIDDLE LEVEL • QUANTITATIVE

Use divisibility rules to test a number.

Learn quick tricks to check if numbers divide evenly without doing long division.

SECTION 1

A Quick Look at the Past

Long ago, people needed fast ways to check big numbers. Divisibility rules are like secret shortcuts from ancient math whizzes. They help you see if one number goes into another without leftovers.

300 BC
Euclid's Ideas
Greek mathematician Euclid wrote about factors in his book. He helped start number rules.
800 AD
Indian Math Wizards
Scholars in India shared digit sum tricks for 3 and 9. These spread worldwide.
1600s
Europe Adopts Them
Math books in Europe added rules for 2, 5, and 10. Kids like you started learning them.
Today
SSAT Prep
These rules save time on tests like the SSAT. You can master them now!

Before computers, these rules helped traders and builders. Now they help you on tests. Let's dive in! You will feel like a math detective.

SECTION 2

What Are Divisibility Rules?

A divisibility rule tells if one number divides evenly into another. It means no remainder, like 12 into 36 perfectly.

1

Even Split

The big number splits into equal groups with nothing left over.
2

Fast Check

Skip long division. Use digit tricks instead. It's like a game cheat code.
3

Common Ones

Rules work best for small numbers like 2, 3, 5, and 9.
4

Practice Wins

Memorize them like your favorite video game moves. You will ace the SSAT!
⚡ Quick Tip
Divisibility rules are like checking if a backpack fits in a locker. Peek at key spots instead of trying every time.
SECTION 3

See the Rules in Action

This diagram shows examples for rules 2, 3, 5, and 9. Highlights mark the key digits to check.

Look at the diagram above. Each box shows a number and the trick to check it. Practice spotting the clues! It's fun like finding hidden objects in a picture.

SECTION 4

How the Math Works

Behind the tricks is simple math called modulo (short for remainder). If n ÷ d has no remainder, it's divisible.

DIVISIBILITY TEST
n mod d = 0
n = big number, d = divisor like 3. Zero remainder means yes!
SUM FOR 3
Sum(digits of n) mod 3 = 0
Why? 10 ≡ 1 mod 3, so powers of 10 act like 1. Easy add-up!

These rules use patterns in base 10. You don't need to know why yet. Just use them to save time! Great job learning this.

SECTION 5

All the Main Rules

Chart lists rules for 2,3,4,5,6,9,10 with tests and examples. Each row highlights one rule.

The chart above breaks down each rule. Pick the one you need and check fast. You are getting good at this! Keep going.

SECTION 6

Step-by-Step: Test 456 for 3, 4, 9

Is 456 divisible by 3? By 4? By 9?
1
Step 1: For 3Sum digits: 4 + 5 + 6 = 15. 15 ÷ 3 = 5, no remainder. Yes!
Yes for 3
2
Step 2: For 4Last two digits: 56. 56 ÷ 4 = 14, exact. Yes!
Yes for 4
3
Step 3: For 9Sum is 15. 15 ÷ 9 = 1 remainder 6. No.
No for 9

See how easy? You just used three rules. You can do this on any number!

SECTION 7

Why Rules Rock (and Limits)

Pros and cons of using rules.
StrengthLimit
Super fast for big numbers. No rule for 7 or 11 easily.
Saves time on SSAT tests. Need to memorize a few.
Fun and like magic tricks. Always double-check with division sometimes.
🏆 KEY TAKEAWAY
Rules are your speedy sidekick in math battles, like a quick dodge in soccer.
SECTION 8

Next Level: Bigger Ideas

Basic RuleAdvanced Way
Sum digits for 3/9Prime factors (3×3=9)
Last digit for 2/5Modulo math for any number
Quick testFull prime check

Rules lead to cool stuff like finding primes. You are on your way there! Keep practicing.

SECTION 9

Test Yourself!

PROBLEM 1 — CONCEPTUAL
Which rule checks if a number is divisible by 5? (A) Sum of digits ÷5 (B) Ends in 0 or 5 (C) Last digit even (D) Last two digits ÷5 (E) Ends in even digit
PROBLEM 2 — BASIC CALCULATION
Is 234 divisible by 2? (A) Yes (B) No (C) Check sum (D) Check last two (E) Ends in 5
PROBLEM 3 — INTERMEDIATE
Is 567 divisible by 3? Sum=5+6+7=18. (A) Yes (B) No (C) Check for 9 (D) Last digit (E) No, 18 not ÷3
PROBLEM 4 — APPLIED
Which is divisible by 4? (A) 123 (B) 456 (C) 789 (D) 101 (E) 222
PROBLEM 5 — CRITICAL THINKING
Is 999 divisible by 9 and 3? (A) 9 yes, 3 no (B) Both yes (C) Both no (D) 9 no, 3 yes (E) Check 2
⭐ You Rock!
Review wrong ones. Practice makes perfect for SSAT.
SUMMARY

Review Time

Master divisibility rules for 2 (even end), 3/9 (digit sum), 4 (last two), 5/10 (0/5 end), 6 (2+3). They save test time!

Use visuals and steps. You are ready for SSAT success. Believe in yourself!

  • Practice daily
  • Check big numbers fast
  • Ace the Quantitative section
Varsity Tutors • SSAT Middle Level • Use divisibility rules to test a number.