Exercise 1.1: Euclid's Division Lemma
You'll use Euclid's division algorithm to find the HCF of pairs of numbers. This exercise builds a strong foundation for understanding how division and remainders connect to factors.
Extra Practice Questions
These questions cover the same concepts as Exercise 1.1. Try solving them to build confidence before or after the textbook exercise.
If LCM(a, b) = 180 and HCF(a, b) = 3, and a = 45, find b.
Show that the cube of any positive integer is of the form 9m, 9m+1, or 9m+8. How many cases need to be checked?
Three bells ring at intervals of 9, 12, and 15 minutes. If they ring together at 8:00 AM, when will they next ring together?
Prove that 3 + 2sqrt(5) is irrational. The proof assumes it is rational, i.e., 3 + 2sqrt(5) = p/q. What contradiction arises?
The HCF of 65 and 117 is expressible in the form 65m - 117. Find the value of m.
There is a circular path around a park. A takes 18 minutes and B takes 12 minutes to complete one round. If they start together, after how many minutes will they meet at the starting point again?
If the HCF of 408 and 1032 is expressible in the form 1032p - 408 x 5, find p.
Which of the following is an irrational number?
The HCF of two prime numbers is always:
Prove that 1/(sqrt(2)) is irrational. Which method is most appropriate?
Stuck on a question?
Paste any question from Exercise 1.1 into our AI Maths Solver and get a step-by-step solution instantly. It works for all NCERT questions.
Try AI Solver — FreeCommon Mistakes to Avoid
- ✗Forgetting to continue the algorithm until the remainder is 0
- ✗Mixing up dividend and divisor in the first step
- ✗Not verifying the HCF by checking it divides both numbers
Other Exercises in Chapter 1
Frequently Asked Questions
How many questions are in NCERT Class 10 Exercise 1.1?
Exercise 1.1 has 4 questions based on Euclid's Division Lemma and finding HCF using the division algorithm.
Is Exercise 1.1 important for CBSE board exams?
Yes, Euclid's Division Lemma is frequently tested. Expect 1-2 mark questions on finding HCF using this method.
What is Euclid's Division Lemma?
For any two positive integers a and b, there exist unique integers q and r such that a = bq + r where 0 ≤ r < b. This is the basis for finding HCF.
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