Number System
0/10 problems solved
Formulas & 30-Second Shortcut Tricks
Formulas
- Divisible by 3/9: digit sum divisible by 3/9; by 11: alternate-digit difference divisible by 11
- HCF × LCM = product of two numbers
- Number of factors of p^a·q^b = (a+1)(b+1)
- Unit digit cycles: 2→(2,4,8,6), 3→(3,9,7,1), 7→(7,9,3,1), 8→(8,4,2,6)
Shortcuts
- Unit digit of a^n: use n mod 4 (0 ⇒ 4th in cycle).
- Sum of first n natural numbers = n(n+1)/2.
Practice problems
Q1
What is the unit digit of 3^41?
Q2
The HCF of two numbers is 8 and their product is 960. What is their LCM?
Q3
Find the sum of the first 50 natural numbers.
Q4
What is the unit digit of 2^63?
Q5
The HCF of two numbers is 4 and their product is 480. What is their LCM?
Q6
Find the sum of the first 20 natural numbers.
Q7
What is the unit digit of 7^57?
Q8
The HCF of two numbers is 4 and their product is 576. What is their LCM?
Q9
Find the sum of the first 40 natural numbers.
Q10
What is the unit digit of 3^60?
Number System Speed Test
1 minute per question. Use the palette to jump around; you'll see time spent on every question at the end.