Question 1 :
Find the LCM and HCF of the following integer by applying the prime factorisation method: 17, 23 and 29
Question 2 :
How is 7429 expressed as a product of its prime factors?
Question 5 :
State true or false: The square of any positive integer is either of the form 4q or 4q + 1 for some integer q.
Question 6 :
Without actually performing the long division, state whether $\frac{64}{455}$ will have a terminating decimal expansion or a non-terminating repeating decimal expansion.
Question 7 :
Using Euclid’s division algorithm, find if this pair of number is co-prime: 231, 396 .
Question 8 :
Every ______________can be expressed ( factorised) as a product of primes, and this factorisation is unique, apart from the order in which the prime factors occur.
Question 9 :
State True or False, Let x = $\frac{p}{q}$, where p and q are coprimes, be a rational number, such that the prime factorisation of q is not of the form $2^n5^m$, where n, m are non-negative integers. Then, x has a decimal expansion which is non-terminating repeating (recurring).
Question 10 :
“The product of three consecutive positive integers is divisible by 6'. Is this statement true or false ?
Question 11 :
How is 5005 expressed as a product of its prime factors?
Question 12 :
Every positive even integer is of the form 2q, and that every positive odd integer is of the form 2q + 1, where q is some integer. TRUE or FALSE ?
Question 13 :
Without actually performing the long division, state whether $\frac{17}{8}$ will have a terminating decimal expansion or a non-terminating repeating decimal expansion.
Question 16 :
A positive integer is of the form 3q + 1, q being a natural number. Can you write its square in any form other than 3m + 1, i.e., 3m or 3m + 2 for some integer m?
Question 19 :
Euclid’s division lemma states that for two positive integers a and b, there exist unique integers q and r such that a = bq + r, where r must satisfy
Question 20 :
Choose the correct answer from the given four options in the question: For some integer m, every even integer is of the form.