Certificates / Quantitative aptitude / Number System
Number System: lesson, then the certificate test
Step 1: the lesson (about 1 min)
Divisibility rules, HCF and LCM, and the unit-digit cycle answer most number questions quickly.
- Divisible by 3 or 9: the digit sum is. By 4: the last two digits are. By 8: the last three digits are. By 11: the difference of alternate-digit sums is 0 or a multiple of 11.
- For TWO numbers, HCF × LCM = their product.
- Unit digits of powers repeat in cycles of 4 (for 2, 3, 7, 8) — divide the power by 4 and use the remainder.
Worked example
What is the unit digit of 7^23?
- Unit digits of 7, 7², 7³, 7⁴: 7, 9, 3, 1 — a cycle of 4
- 23 ÷ 4 leaves remainder 3
- The third in the cycle is 3
Answer: 3
Watch out
- HCF × LCM = product works only for two numbers, not three.
Made by Shishya (AI-assisted): a general method in our own words, with our own example; no exam or platform question is copied.
Step 2: the test
- 15 questions from Shishya's checked question bank, 20 minutes. Pass mark: 11 correct.
- Scored on Shishya's server; the answers are not shown afterwards, so the test stays fair. Each attempt draws new questions.
- Free. Your first test needs no account; sign up free to take more. Your answers and score are not stored; if you pass, you choose the name to print (ages 13 and up).
- It is a Shishya completion certificate — not a university or government credential. The test is not supervised.