Divisibility Rules For 13 - Vedantu

The concept of Divisibility Rules for 13 plays a key role in mathematics and is widely applicable to both real-life situations and exam scenarios. This rule helps students quickly check if a number can be divided by 13 without using direct division, saving time in calculations and competitive exams.

What Is the Divisibility Rule for 13?

A divisibility rule for 13 is a simple mathematical shortcut that lets you test whether a number is exactly divisible by 13. You’ll find this concept applied in topics such as number theory, quick calculation tricks, and factorization. The rule avoids long division, making it handy during timed quizzes, Olympiads, and exams like JEE or NTSE.

Key Formula for Divisibility by 13

Here’s the standard formula: Remove the last digit from the number, multiply that digit by 9, and add the result to the truncated number. If the answer is divisible by 13 (including 0), the original number is divisible by 13.

Cross-Disciplinary Usage

Divisibility rules for 13 are not only useful in Maths but also help in Physics equations, coding (for checking cycles or periodicity), and logical puzzles that require pattern recognition. Students preparing for JEE or NEET will see its relevance when simplifying large numerical expressions.

Step-by-Step Illustration

1. Let’s take the number 858. Step 1: Remove the last digit (8). Remaining number = 85. Step 2: Multiply the last digit by 9 → 8 × 9 = 72. Step 3: Add 72 to the remaining number 85 → 85 + 72 = 157. Step 4: Repeat the process if needed: Remove last digit: 7, remaining: 15; 7 × 9 = 63; 15 + 63 = 78. Since 78 is divisible by 13 (13 × 6), the original number 858 is divisible by 13.

Alternative Rules for 13 (Quick Table)

Rule	Description	Example (for 286)
Rule 1	Multiply last digit by 9, add to rest	28 + (6 × 9) = 28 + 54 = 82 (repeat: 8 + 2 × 9 = 26, which is 2 × 13)
Rule 2	Multiply last digit by 4, add to rest	28 + (6 × 4) = 28 + 24 = 52 (52/13 = 4)
Rule 3	Alternating sum of 3-digit groups	(for larger numbers, like 2,453,674: 674 - 453 + 2 = 223)
Rule 4	Subtract last two digits from 4 × other digits	(28 × 4) - 6 = 112 - 6 = 106

Speed Trick or Vedic Shortcut

Here’s a quick shortcut for the divisibility rule for 13 many students use during exams:

1. Take the last digit of the number.
2. Multiply it by 9 and add to the remaining number (as per the rule).
3. If the result is big, repeat the steps until you get a small number.
4. If that small number is divisible by 13, so is your starting number!

These tricks work in NTSE, Olympiads, and fast classroom quizzes. Vedantu’s live classes share more such mental math techniques for all divisibility rules.

Try These Yourself

• Check if 390 is divisible by 13.
• Is 728 divisible by 13?
• Find out if 1690 passes the divisibility rule for 13.
• Name three 3-digit numbers divisible by 13.

Frequent Errors and Misunderstandings

• Forgetting to repeat the process until a small, checkable number.
• Multiplying by the wrong number (it’s 9 for trick 1, not 13 itself).
• Applying the rule for divisibility by 3 or 11 instead of 13 by mistake.

Relation to Other Concepts

The idea of divisibility rules for 13 connects with factors, multiples, prime numbers, and the general divisibility rules for Maths. Mastering this helps with finding HCF, LCM, and solving number-based puzzles.

Classroom Tip

A quick way to remember: “Multiply the last digit by 9, add to the rest, check again!” Repeat until you see a familiar multiple of 13. Ask your teacher for a number chain or table to help in practice. Vedantu’s classes include printable tables for all tricky divisibility rules.

Summary Table: Rule, Example, Shortcut

Rule Name	Process	Example Number	Result
Multiply last digit by 9, add	Truncate last digit, multiply by 9, add	858	858 → 85+72=157 → 15+63=78 → 78/13=6
Multiply last digit by 4, add	Truncate last digit, multiply by 4, add	650	65+0=65 (divisible by 13: 5)
Subtract last two digits from 4×rest	(Other digits)×4 - (last two digits)	728	7×4=28, 28-28=0; 0 is divisible by 13
Alternating sum, blocks of three	Sum 3-digit blocks alternately	2,453,674	674-453+2=223 (not divisible by 13)

We explored Divisibility Rules for 13—from definition, formulas, examples, common mistakes, and how it links to other Maths topics like factors, multiples, and primes. Continue practicing with Vedantu to become quick and confident with divisibility skills for all numbers.

Divisibility Rules Full Guide | Factors of 13 | Multiples of 13 | Practice Divisibility Questions