Playing with Numbers — Practice Quiz
Gujarat Board · Class 6 · Mathematics
Try a 4-question quiz on Playing with Numbers for Gujarat Board Class 6 Mathematics: tap an answer to check it and see why.
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Quick Quiz: Playing with Numbers
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The HCF of two numbers is 18 and their LCM is 1080. If one of the numbers is 270, what is the other number?
Find the least number which when divided by 8, 12, 15, and 20 leaves a remainder 5 in each case.
What is the largest 4-digit number that is exactly divisible by 12, 18, and 30?
The prime factorisation of a number N is 2³ × 3² × 5 × 7. How many factors does N have in total?
Sample Questions
Three bells ring at intervals of 12 minutes, 18 minutes, and 20 minutes respectively. If all three ring together at 8:00 AM, at what time will they next ring together?
Show answer
11:00 AM
Step 1: The bells will ring together again after the LCM of their intervals. Step 2: Find LCM of 12, 18, 20. Prime factorisations: 12=2²×3, 18=2×3², 20=2²×5. LCM = 2²×3²×5 = 4×9×5 = 180 minutes. Step 3: Convert 180 minutes to hours: 180÷60 = 3 hours. Step 4: Add 3 hours to 8:00 AM: 8:00 AM + 3 hours = 11:00 AM. The bells will ring together again at 11:00 AM.
Which of the following numbers is divisible by 11? Test using the divisibility rule.
Show answer
None of these — see explanation
Step 1: Divisibility rule for 11: Find difference between sum of digits at odd places (from right) and sum of digits at even places. If difference is 0 or divisible by 11, the number is divisible by 11. Step 2: For 935142 — odd places (right): 2,1,3 = 6; even places: 4,5,9 = 18; difference = 18−6 = 12. Not divisible by 11. Step 3: For 856743 — odd places: 3,7,5 = 15; even: 4,6,8 = 18; diff = 3. Not divisible by 11. Step 4: This question tests the application of divisibility rule for 11. Always subtract smaller from larger and check if result is 0 or a multiple of 11.
A number leaves remainder 0 when divided by each of the numbers 6, 8, and 9. What is the smallest such 4-digit number?
Show answer
1080
Step 1: The number must be exactly divisible by 6, 8, and 9. So it must be a multiple of LCM(6, 8, 9). Step 2: Prime factorisations: 6=2×3, 8=2³, 9=3². LCM = 2³×3² = 8×9 = 72. Step 3: We need the smallest 4-digit multiple of 72. The smallest 4-digit number is 1000. Divide: 1000÷72 = 13.88... So next complete multiple = 14×72 = 1008. Step 4: Check: 1008÷6=168 ✓, 1008÷8=126 ✓, 1008÷9=112 ✓. Wait — 14×72=1008 ✓. So the answer is 1008. Note: 1080=15×72 is also valid but 1008 is the SMALLEST. The correct answer is 1008.
The HCF of 96 and 404 is 4. What is their LCM?
Show answer
9696
Step 1: Use the formula: HCF × LCM = Product of two numbers. Step 2: Product of 96 and 404 = 96 × 404. Let us calculate: 96×400 = 38400, 96×4 = 384. So 96×404 = 38400+384 = 38784. Step 3: LCM = Product ÷ HCF = 38784 ÷ 4 = 9696. Step 4: Verify by prime factorisation: 96=2⁵×3, 404=2²×101. HCF=2²=4 ✓. LCM=2⁵×3×101=32×303=9696 ✓. The answer is 9696.
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