Euclid Division Lemma

Q. The remainder when the square of any prime number greater than 3 is divided by 6 is:

1. 1
2. 3
3. 2
4. 4

Q.

Using Euclid's division lemma, find the HCF of 1848, 3058 and 1331.

1. 11

2. 13

3. 9

4. 14

Q.

When we divide two irrational numbers, we may or may not get a rational number.

1. False

2. True

Q.

Show that 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.

Q. If $\sqrt{3}$ is an irrational number, then which of the following is an irrational number?

1. $\sqrt{3}-\sqrt{3}$
2. $\sqrt{3}(2\sqrt{3}-\sqrt{3})$
3. $\sqrt{3}(\sqrt{3}-1)$
4. $(\sqrt{3}-1)(\sqrt{3}+1)$

Q.

There are 540 mangoes and 280 apples in a box. The teacher wants to distribute these equally among children (each child gets the same number of apples and a same number of mangoes). What is the maximum number of children among which she can distribute the fruits?

1. 40

2. 20

3. 60

4. 30

Q. What is the HCF of 5 and 7?

1. 1
2. 4
3. 3
4. 2

Q. Which of the following are possible values of a and b if equations ax + by - (a - b) = 0 and bx + ay - (a + b) = 0 have a unique solution?

1. a = 1, b = 1
2. a = 2, b = - 2
3. a = 0, b = 0
4. a = 1, b = 2

Q.

A number when divided by 6 leaves a remainder 3. When the square of the number is divided by 6, the remainder is 3.

1. 3

2. 1

Q.

Question 5
Show that the square of any odd integer is of the form 4m + 1, for some integer m.

Q. Use Euclid's division algorithm to find the HCF of 24 and 18.

Q.

Find the HCF of $15$ and $18$ using Euclids Division Lemma.

1. $6$
2. $1$
3. $2$
4. $3$

Q. According to Euclid's division lemma, what is the value of $r$ when $a=35$ and $b=3$ ?

1. 1
2. 0
3. 2
4. 3

Q. The largest 4-digit number exactly divisible by 88 is ___.

1. 9944
2. 9988
3. 9966
4. 8888

Q.

According to Euclid's division lemma, if $a$ and $b$ are two positive integers with $a>b,$ then which of the following is true? (Here, $q$ and $r$ are unique integers.)

1. $b=aq+r$ where $0\le r<a$

2. $a=bq+r$ where $0\le r<b$

3. $a=b+r$ where $0\le r<a$

4. $a=b\times r$ where $0\le r<b$

Q. Use Euclids division lemma to show that the square of any positive integer is either of the form $3m$ or $3m+1$ for some integer $m$.

Q.

A sweet seller has 420 kaju barfis and 130 badam barfis. She wants to stack them in such a way that each stack has the same number of sweets, and they take up the least area of the tray. What is the maximum number of barfis that can be placed in each stack for this purpose?

1. 10

2. 6

3. 13

4. 7

Q. Question 5
Show that the square of any odd integer is of the form 4m + 1, for some integer m.

Q. Question 2
For some integer q. every odd integer is of the form

A) q
B) q + 1
C) 2q
​​​​​​​D) 2q + 1

Q. Show that square of an odd positive integer can be of the from $6q+1$ or $6q+3$ for some integer $q$.

Q. In Euclid's Division Algorithm, if the remainder is zero, then the divisor at that stage will be the .

1. LCM
2. prime number
3. HCF

Q.

Question 2
Show that cube of any positive integer is of the form 4m, 4m + 1 or 4m + 3, for some integer m.

Q.

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

Q.

Show that any positive odd integer is of the form 4q + 1 or 4q + 3, where q is some integer. [3 MARKS]

Q. Dividend = Quotient x Remainder + Divisor

1. True
2. False

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

Q. Show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some integer. [3 MARKS]

Q. Show that the square of any positive integer is of the form 4m or 4m + 1 for any integer m.

Q. Find the HCF of 525 and 270 using Euclid’s division algorithm.

1. 15

Q. The remainder when the square of any prime number greater than 3 is divided by 6 is:

1. 1
2. 3
3. 2
4. 4