Divisibility rules for 3, 4, 9 and 11: Class 6 practice
Divisibility rules let you test a number without dividing: by 3 or 9 if the digit sum is; by 4 if the last two digits are; by 11 if the difference between alternate digit sums is 0 or a multiple of 11.. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Place value
- Addition of digits
The idea behind divisibility rules for 3, 4, 9 and 11
Divisibility rules let you test a number without dividing: by 3 or 9 if the digit sum is; by 4 if the last two digits are; by 11 if the difference between alternate digit sums is 0 or a multiple of 11.
Step-by-step method
- Pick the rule for the divisor.
- Apply it to the digits.
- Decide yes or no and state the reason.
Worked example 1 (Basic)
Without dividing, is 27026 divisible by 3?
- Digit sum = 17
- This fails the test for 3
- Answer: No
Worked example 2 (Standard)
Without dividing, is 29682 divisible by 4?
- Last two digits 82
- This fails the test for 4
- Answer: No
Worked example 3 (Challenge)
Without dividing, is 59376 divisible by 11?
- Alternate sums 14 and 16, difference -2
- This fails the test for 11
- Answer: No
Common mistakes and misconceptions
- Using the digit-sum rule for 4
- Starting the alternate sums inconsistently for 11
Practice questions
- (Basic) Without dividing, is 76122 divisible by 3?
- (Basic) Without dividing, is 34810 divisible by 3?
- (Standard) Without dividing, is 78927 divisible by 4?
- (Standard) Without dividing, is 50696 divisible by 4?
- (Challenge) Without dividing, is 33128 divisible by 11?
- (Challenge) Without dividing, is 89614 divisible by 11?
Answer key with full working
- Q1: Digit sum = 18 → This passes the test for 3 → Answer: Yes
- Q2: Digit sum = 16 → This fails the test for 3 → Answer: No
- Q3: Last two digits 27 → This fails the test for 4 → Answer: No
- Q4: Last two digits 96 → This passes the test for 4 → Answer: Yes
- Q5: Alternate sums 12 and 5, difference 7 → This fails the test for 11 → Answer: No
- Q6: Alternate sums 18 and 10, difference 8 → This fails the test for 11 → Answer: No
Syllabus note
This skill is listed under "Playing with Numbers" for Class 6 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.
Related practice and notes
Frequently asked questions
Which chapter is divisibility rules for 3, 4, 9 and 11 in?
"Playing with Numbers", Class 6 Maths (NCERT/CBSE). Other boards may place it differently.
How were the answers checked?
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.