Fill in the Blanks

1). H.C.F. of 6, 72 and 120 is ________________.

6

2). 156 as a product of its prime factors _____________

`2^{2}\times3\times13`

3). If a = bq + r, least value of r is ________________.

Zero

4). If every positive even integer is of the form 2q, then every positive odd integer is of the form _________, where q is some integer.

2q + 1

5). The exponent of 2 in the prime factorisation of 144, is _____________.

4

6). `\sqrt{2}`, `\sqrt{3}`, `\sqrt{6}`, etc are _____________ numbers.

Irrational

7). `7\sqrt{5}` is a/an ___________ number.

Irrational

8). An algorithm which is used to find HCF of two positive numbers is ______________.

Euclid’s division algorithm

9). `6+\sqrt{2}` is a/an ____________ number.

Irrational

10). Every point on the number line corresponds to a ______________ number.

Real

11). A ___________ is a proven statement used for proving another statement.

lemma

12). The product of three numbers is _____________ to the product of their HCF and LCM.

Not equal

13). L.C.M. of 96 and 404 is ________________.

9696

14). If p is a prime number and it divides `a^{2}` then it also divides ___________, where a is a positive integer.

a

15). `\frac{35}{50}` is a __________ decimal expansion.

terminating

16). An ___________ is a series of well defined steps which gives a procedure for solving a type of problem.

algorithm

17). Every real number is either a ___________ number or an ___________ number.

Rational, Irrational

18). Euclid’s Division Lemma is a restatement of ______________.

Long division process

19). `\frac{1}{\sqrt{2}}` is a/an ___________ number.

Irrational

20). Numbers having non-terminating, non-repeating decimal expansion are known as _____________.

Irrational numbers

21). `\sqrt{5}` is a/an ………. number. 

irrational

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