Euclid Division Algorithm

Q.

Use Euclids Division Lemma to show that the square of any positive integer is either $5n,5n+1or5n+4$ for some integer.

Q.

Which is the largest number that perfectly divides 480 and 270?

1. 60

2. 30

3. 10

4. 15

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

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.

Question 1
For some integer m, every even integer is of the form

A) m
B) m + 1
C) 2m
D) 2m + 1

Q.

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

1. 3, 9

2. 8, 16

3. 16, 5

4. 18, 75

Q. Show that every positive integer is either even or odd..

Q.

Visualizing Euclid’s division algorithm, find the values of $a,b$ and $c.$

1. $a=11,b=8,c=4$

2. $a=12,b=12,c=3$

3. $a=13,b=11,c=2$

4. $a=10,b=12,c=5$

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

Q. All the faces of a cube are painted with blue colour. Then it is cut into 125 small equal cubes. How many small cubes will be formed having no face coloured ?

1. 27
2. 24
3. 8
4. 16

Q.

Question 1
For some integer m, every even integer is of the form

A) m
B) m + 1
C) 2m
D) 2m + 1

Q. The HCF of 135 and 225 is .

1. 35
2. 45
3. 25

Q. A seminar is being conducted by an Educational Organisation, where the participants will be educators of different subjects. The number of participants in Hindi, English and Mathematics are 60, 84 and 108 respectively.
The product of HCF and LCM of 60, 84 and 108 is

Q. Geeta planned to floor her living room of size $520\text{cm}\times 300$ cm with the least number of square tiles of equal areas. If the cost for tiling is ₹ 64/tile, find the total cost incurred on tiling.

1. ₹ 18, 000
2. ₹ 24, 960
3. ₹ 15, 600
4. ₹ 18, 200

Q. What is the least number that must be subtracted from 1056 so the number is divisible by 23?

1. 18
2. 19
3. 21
4. 22

Q.

The least multiple of 7 which leaves a remainder of 4, when divided by 6, 9, 15 and 18 is ___.

1. 364

2. 74

3. 94

4. 184

Q. According to Euclid's division lemma, the remainder has to be the divisor.

1. greater than
2. lesser than
3. equal to