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Euclidโs division algorithm can be applied to :
Euclidโs division algorithm can be applied only to positive integers.
For some integer m, every even integer is of the form :
Integer are 2, 4, 6, 8โฆ. It can be written in the form of 2m. Where m = integer.
If the HCF of 65 and 117 is expressible in the form 65m โ 117, then the value of m is :
HCF
If two positive integers \(p \) and \(q \) can be expressed as \(p=ab^2 \) and \(q = a^3b, a; b\) being prime numbers, then \(LCM\ (p, q)\) is :
LCM
The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is :
LCM of numbers from 1 to 10
\(7\times11\times13\times15+15 \) is:
which is a composite number.
\(1.23\bar{48} \) is:
is a rational number as can be expressed in form
\(2.\bar{35} \) is:
is a rational number
3.24636363… is :
It is a rational number as real as nonterminating repeating decimal number.
If the HCF of 85 and 153 is expressible in the form 85m โ 153, then the value of m is :
The decimal expansion of the rational number \(\dfrac{47}{2^2.5} \) will terminate after :
It will terminate after two decimal places
If two positive integers \(p \) and \(q \) can be expressed as \(p = ab^2\) and \(q = a^2b; a, b\) being prime numbers, then \(LCM\ (p, q)\) is :
LCM =
Euclidโs division lemma states that for two positive integers a and b, there exist unique integers q and r such that a = bq + r, where :
Following are the steps in finding the GCD of 21 and 333 :
\(333=21\times m+18\\ \\ 21=18\times1+3\\ \\ n=3\times6+0 \)
The integers \(m \) and \(n \) are :
\((n+1)^21 \) is divisible by 8, if n is :
is divisible by 8 if n is an even integer.
The largest number which divides 71 and 126, leaving remainders 6 and 9 respectively is :
let us subtract 6 and 9 from 71 and 126, i.e.
and
now find the hcf of 65 and 117.
thus the hcf of 65 and 117 is 13 and the required number is 13.
If two integers \(a \) and \(b \) are written as \(a=x^3y^2 \) and \(b=xy^4;x,y \) are prime numbers, then H.C.F. \((a,b) \) is:
HCF
The decimal expansion of the rational number \(\dfrac{14517}{1250} \) will terminate after :
So it will terminate after 4 decimal places.
Which of the following rational numbers have a terminating decimal expansion ?
have a terminating decimal expansion as it can be expressed in the form of
The value of \(x \) in the factor tree is :
\(\begin{tikzpicture}[+preamble]\usepackage{forest}[/preamble]\begin{forest}[x 5 ] [ 5] [ 2 ][3]]]]\end{forest}\end{tikzpicture} \)
If two positive integers \( a\) and \(b \) are written as \(a=x^2y^2 \) and \(b=xy^2;x,y \) are prime number then HCF \((a,b) \) is:
HCF
\(n^21 \) is divisible by \(8 \), if \(n \) is :
is divisible by 8 if is an odd integer
\(x=2^2\times3\times5^2,y=2^2\times3^3 \), then HCF \((x,y) \) is
HCF
The decimal expansion of the rational number \(\dfrac{11}{2^3.5^2} \) will terminate after :
It will terminate after 3 decimal places
How many prime factors are there in prime factorisation of 5005 ?
If least prime factor of a is 3 and least prime factor of b is 7, the least prime factor of (a + b) is:
Least factor of 10 is 2
\(119^2111^2 \) is:
which is a composite number
The decimal expansion of \(\dfrac{6}{1250} \) will terminate after how many places of decimal ?
It will terminate after 4 decimal places.