Real Numbers-Class 10

1) To find the HCF of 867 and 255 using Euclid's Division Algorithm, the first step is:

2) The Fundamental Theorem of Arithmetic states that every composite number can be uniquely expressed as a product of

3) Using Euclid's Algorithm, the HCF of 45 and 75 is:

4) If HCF(a, b) = 1, then LCM(a, b) is equal to:

5) Substituting p = 2k in p^2 = 2q^2, we get 4k^2 = 2q^2, which simplifies to:

6) The prime factorization of 360 is:

7) To prove that √2 is irrational, we assume that √2 is:

8) According to Euclid's Division Lemma, if a = 13 and b = 4, then the remainder 'r' is:

9) Using Euclid's Division Lemma, if a number is divided by 5, the possible remainders are:

10) The product of a non-zero rational number and an irrational number is always:

11) The LCM of 8, 9, and 25 is:

12) Which of the following statements is true?

13) If the HCF of two numbers is found using Euclid's Division Algorithm, the process continues until the remainder becomes:

14) The number of rational numbers between any two distinct rational numbers is:

15) According to Euclid's Division Lemma, for any integer 'a' and positive integer 3, 'a' can be written in the form 3q, 3q + 1, or:

16) The HCF of two numbers 'a' and 'b' is the largest positive integer that divides both 'a' and 'b'. This is the:

17) The HCF of 135 and 225 using Euclid's Division Algorithm will have the last non-zero remainder as the:

18) The sum of two rational numbers is always:

19) The HCF of two consecutive positive integers is always:

20) The LCM of two numbers 'a' and 'b' is the smallest positive integer that is divisible by both 'a' and 'b'. This is the: