Euclid's Division Algorithm

Q.

Find the smallest $4$ digit number divisible of $18,24$ and $32$.

Q.

Krishnan bought chocolates for his brothers. When he grouped the chocolates in groups of 4, 1 chocolate was left, if grouped in 5, 4 chocolates were left, if grouped in 6, 1 chocolate was left and if grouped in 7, no chocolate was left ungrouped. If the total number of chocolates bought was less than 50, find the number of chocolates Krishnan bought.

1. 49

2. 35

3. 45

4. 29

Q.

$\text{If HCF (1008, 20) = HCF (20, a)}\text{= HCF(a, b) where}1008=20\times q+a\text{and}20=a\times m+b.$

Here, q, a, m and b being positive integers satisfying Euclid’s division lemma. What could be the values of a and b?

1. 8, 4

2. 10, 4

3. 20, 8

4. 24, 8

Q.

The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and 15 as remainder. What is the smaller number ?

1. 270

2. 240

3. 295

4. 360

Q.

2361 = ( 784 $\times$ Q ) + R
Find the value of Q and R.

1. 7, 366

2. 18, 758

3. 16, 758

4. 758, 16

Q.

Prove that if a positive number is of the form $6q+5$, then it is of the form $3q+2$ for some integer, but not conversely

Q. If n is positive even integer, then $n(n+1)(n+2)$ is ................

1. a prime number
2. divisible by 24
3. divisible by 16
4. divisible by 20

Q.

The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and 15 as remainder. What is the smaller number ?

1. 295

2. 270

3. 240

4. 360

Q.

If the HCF of $65$ and $117$ is expressible in the form $65\mathrm{m}-117$, then the value of $\mathrm{m}$ is

1. $4$

2. $2$

3. $1$

4. $3$

Q.

If in a class there are $30$ girls and $18$ boys, then

Strength : Number of boys $=$______

Q. SHOW THAT n^3 - n IS DIVISIBLE BY 8 , FOR ANY POSITIVE INTEGER n

Q. Use Euclids division lemma to find the H.C.F of the following.

(i) 16 and 176

Q.

What is the logarithm of a negative number?

Q. If $2\log x-\log y=1$ is $x^2=my$, then value of $m$ is equal to

1. $5$
2. $10$
3. $20$
4. $15$