Class 8 Maths · Original EZT practice
Number Play (Class 8 Chapter 5): summary and practice
Is four thousand five hundred thirty-six a multiple of nine? You can tell without dividing. Chapter 5 builds quick tests for divisibility and uses them in digit puzzles. All questions are original EZT tutor practice following the chapter's own section order. Edition note: this page covers the new NCERT book Ganita Prakash (Grade 8). Older Class 8 books numbered chapters differently - check your chapter title, not just the number.
8 original worked examples, 8 fresh self-check questions and 4 mixed questions, with explained answers. These are not copied textbook exercises, an official chapter index or a full answer key. No affiliation with NCERT is claimed.
Official sources for topic and edition context, checked 20 October 2026:
1. Is this a multiple of?
If a number divides two numbers, it divides their sum and their difference. And if a number is divisible by both nine and four, it is divisible by thirty-six, because nine and four share no common factor.
2. Checking divisibility quickly
By two, the last digit is even. By five, the last digit is zero or five. By ten, the last digit is zero. By four, the last two digits form a multiple of four. By eight, the last three digits form a multiple of eight. By three or nine, the digit sum is a multiple of three or nine. By eleven, the difference between the alternate digit sums is zero or a multiple of eleven.
3. Digits in disguise
Replace letters with digits so the arithmetic works. Divisibility tests narrow the choices quickly.
Choose, solve, check, then try a fresh question.
Before calculating, read the method prompt and name the condition that makes it useful. Write your own attempt. Open the steps only when you need them, and use the check to catch a wrong sign, unit or interpretation. Finish with the fresh question before reading its answer.
Use sums of multiples
Choose the method: A common divisor of two numbers also divides their sum and difference.
EZT practice question
Twenty-four and thirty-six are both multiples of twelve. Is their sum a multiple of twelve?
Show the worked solution
- Their sum is sixty.
- Sixty is twelve times five.
Answer: Yes - sixty is twelve times five.
Check: A common divisor of two numbers also divides their sum.
Watch for this: Do not retest each addend separately; the rule settles it in one step.
Now try it yourself
Fifteen and forty-five are multiples of five - is sixty?
Check your answer
Yes - sixty is five times twelve.
The sum of multiples of five is a multiple of five.
Combine two divisibility facts
Choose the method: When the two divisors share no common factor, divisibility by both means divisibility by their product.
EZT practice question
Seventy-two is divisible by nine and by four. Is it divisible by thirty-six?
Show the worked solution
- Nine and four share no common factor.
- So divisibility by both means divisibility by their product, thirty-six.
Answer: Yes - seventy-two is thirty-six times two.
Check: Seventy-two divided by thirty-six is exactly two.
Watch for this: This combination works only when the two divisors share no common factor.
Now try it yourself
Can divisibility by six be checked using two and three together?
Check your answer
Yes - two and three share no common factor.
A number divisible by both two and three is divisible by six.
Check divisibility by nine
Choose the method: Add the digits; the sum must be a multiple of nine.
EZT practice question
Is four thousand five hundred thirty-six divisible by nine?
Show the worked solution
- The digit sum is four plus five plus three plus six, which is eighteen.
- Eighteen is a multiple of nine.
Answer: Yes - the digit sum eighteen is a multiple of nine.
Check: Four thousand five hundred thirty-six is nine times five hundred four.
Watch for this: Do not stop after the first digit sum if it is still large; you can sum its digits again.
Now try it yourself
Is three thousand one hundred forty-one divisible by three?
Check your answer
Yes - the digit sum is nine.
Three plus one plus four plus one is nine, a multiple of three.
Check divisibility by eight
Choose the method: Test only the last three digits.
EZT practice question
Is seven thousand one hundred twenty-eight divisible by eight?
Show the worked solution
- Look at the last three digits: one hundred twenty-eight.
- One hundred twenty-eight is eight times sixteen.
Answer: Yes - the last three digits form a multiple of eight.
Check: Every multiple of one thousand is divisible by eight, so only the last three digits matter.
Watch for this: Do not test only the last digit; eight needs the last three.
Now try it yourself
Is one thousand two hundred thirty-six divisible by four?
Check your answer
Yes - thirty-six is a multiple of four.
Four needs only the last two digits.
Check divisibility by eleven
Choose the method: Subtract the sums of alternate digits.
EZT practice question
Is two thousand seven hundred twenty-eight divisible by eleven?
Show the worked solution
- Alternate digit sums: two plus two is four; seven plus eight is fifteen.
- The difference is eleven.
Answer: Yes - the difference eleven is a multiple of eleven.
Check: Two thousand seven hundred twenty-eight is eleven times two hundred forty-eight.
Watch for this: Use the difference of the alternate sums, not their total.
Now try it yourself
Is eight thousand one hundred seventy-three divisible by eleven?
Check your answer
Yes - eight plus seven is fifteen and one plus three is four; the difference is eleven.
A difference of eleven means divisible by eleven.
Find a missing digit using the three test
Choose the method: Write the digit sum with the unknown letter and pick values that make it a multiple of three.
EZT practice question
The number five-two-A is divisible by three. Find A.
Show the worked solution
- The digit sum is five plus two plus A, which is seven plus A.
- Seven plus A must be a multiple of three.
Answer: A is two, five or eight.
Check: Seven plus two is nine; seven plus five is twelve; seven plus eight is fifteen.
Watch for this: A is a single digit, so stop at eight; the next value would be eleven.
Now try it yourself
The number six-D-two is divisible by three - what could D be?
Check your answer
One, four or seven.
Six plus two plus D is eight plus D, which must be a multiple of three.
Find a missing digit using the nine test
Choose the method: Same idea, with the digit sum a multiple of nine.
EZT practice question
The number three-B-six is divisible by nine. Find B.
Show the worked solution
- The digit sum is three plus B plus six, which is nine plus B.
- Nine plus B must be a multiple of nine.
Answer: B is zero or nine.
Check: Three hundred six and three hundred ninety-six both divide by nine.
Watch for this: Do not forget zero; it is a valid digit here.
Now try it yourself
The number four-C is divisible by nine - find C.
Check your answer
Five - the number is forty-five.
Four plus C must be nine.
Find a missing digit using the four test
Choose the method: Only the last two digits decide divisibility by four.
EZT practice question
The number seven-E-four is divisible by four. Find E.
Show the worked solution
- Only the last two digits matter for four.
- E four must be a multiple of four.
Answer: E is zero, two, four, six or eight - any even digit works.
Check: Four, twenty-four, forty-four, sixty-four and eighty-four are all multiples of four.
Watch for this: Do not test the whole number; four needs only the last two digits.
Now try it yourself
The number five-F is divisible by five - find F.
Check your answer
Zero or five.
Multiples of five end in zero or five.
Try a mixed set
Choose a method or explanation before opening each answer.
1. How do you check divisibility by nine?
Show answer and reason
Add the digits; if the sum is a multiple of nine, the number is.
Digit sums preserve the remainder on division by nine.
2. How do you check divisibility by eight?
Show answer and reason
See whether the last three digits form a multiple of eight.
Every thousand is divisible by eight.
3. How do you check divisibility by eleven?
Show answer and reason
Subtract the alternate digit sums; zero or a multiple of eleven means divisible.
Places alternate sign relative to eleven.
4. If a number is divisible by nine and four, is it divisible by thirty-six?
Show answer and reason
Yes, because nine and four share no common factor.
Coprime divisors combine into their product.
Try it yourself
Work these on paper before checking any notes. Answers are deliberately not shown here.
- Is six thousand three hundred forty-five divisible by nine? By five?
- Is twelve thousand three hundred forty-four divisible by eight?
- The number two-G-seven is divisible by nine. Find G.
Know the rule but lose track of the steps?
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Questions about this practice page
- How do you check divisibility by nine?
- Add the digits; if the sum is a multiple of nine, the number is.
- How do you check divisibility by eight?
- See whether the last three digits form a multiple of eight.
- How do you check divisibility by eleven?
- Subtract the sum of the digits in odd places from the sum in even places; zero or a multiple of eleven means divisible.
- If a number is divisible by nine and four, is it divisible by thirty-six?
- Yes, because nine and four share no common factor.
- Are these the NCERT exercise questions for Number Play (Class 8)?
- No. EZT pages are original practice following the chapter's section order - use them to prepare for the textbook exercises, not as a substitute for your book.