Number System — Divisibility Rules, HCF × LCM, Unit Digit and the Factor-Count Formula

Number system is the quietest scoring chapter in the whole quantitative paper. It carries two to four questions in SSC CGL and CHSL, one or two in Railway NTPC and Group D, and it turns up inside BPSC TRE-4 and CTET mathematics as well. Nobody finds it glamorous, so nobody revises it, and that is exactly why it is worth ten minutes.

What makes it different from percentage or profit and loss is that almost nothing here needs calculation. A divisibility question is answered by looking at two digits. A unit-digit question is answered by dividing the power by 4. A factor-count question is answered by writing one product. If you find yourself doing long division in this chapter, you have missed the rule — and the rule is always shorter than the arithmetic. Four tools cover it: divisibility, HCF and LCM, cyclicity, and factor counting.

1. What is the unit digit of 7¹⁰⁵?

2. The HCF of two numbers is 6 and their LCM is 36. If one number is 12, the other number is —

3. Which of the following numbers is divisible by 11?

4. How many factors does 72 have?

5. The sum of the first 20 odd natural numbers is —

6. What is the smallest number which, when divided by 12, 15 and 20, leaves a remainder of 5 in each case?

7. The LCM of the fractions 2/3, 4/9 and 6/5 is —

8. The number 1 is —