Single Choice

Use Euclid's algorithm to find the HCF of $$4052$$ and $$12576$$.

A
B
C
D
Correct Answer

Solution

According to the definition of Euclid's theorem,
$$a = b \times q + r$$ where $$0 \leq r < b .$$
Using euclid's algorithm

$$12576 = 4052\times 3+420$$
$$4052 = 420 \times 9+272$$

$$420 = 272\times 1+148$$
$$272 = 148\times1+124$$

$$124 = 24\times 5+4$$
$$24=4\times6+0$$

Therefore 4 is the H.C.F of 4052 and 12576

SIMILAR QUESTIONS

Number Systems

$$n^2 -1$$ is divisible by $$8$$ , if n is

Number Systems

If $$n$$ is an odd integer then show that $${n^2} - 1$$ is divisible by 8

Number Systems

Show that the square of any integer is either of the form $$ 4q$$ or $$4q+1$$ for some integer $$q.$$

Number Systems

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 $$m$$? Justify your answer.

Number Systems

Write whether the square of any positive integer can be of the form $$3m+2$$, where $$m$$ is a natural number. Justify your answer.

Number Systems

Show that the square of any positive integer cannot be of the form $$ (6m + 2) $$ or $$ (6m + 5) $$ for any integer $$ m $$ .

Number Systems

Show that the square on any odd integer is of the form $$ (4q + 1) $$ for some integer $$ q $$.

Number Systems

Show that the cube of a positive integer of the form $$ (6q + r) $$ where $$ q $$ is an integer and $$ r = 0 , 1 , 2, 3 , 4 $$ and $$ 5 $$ is also of the form $$ (6m + r) $$.

Number Systems

State Euclid's division lemma and give some examples.

Number Systems

Write whether the square of any positive integer can be of the form $$3m+2$$, where $$m$$ is a natural number. Justify your answer.

Contact Details