Method of Finding HCF

Q.

Find the greatest number of 6 digits exactly divisible by 24, 15, 36.

Q.

Find the largest number which divides 615 and 963 leaving the remainder 6 in each case.

Q.

Find the greatest number that will divide 445, 572 and 699 leaving remainder 4, 5, 6 effectively

Q. Find the least number that is divisible by all the numbers from 1 to 10 (both inclusive).

Q. The largest number which divides 972 and 2016 leaving remainder 15 in each case, is

1. 78
2. 87
3. 3
4. 13

Q.

Two numbers are in the ratio of 15:11. If their H.C.F is 13, the numbers will be:

1. 195 and 143

2. 190 and 140

3. 185 and 163

4. 185 and 143

Q. Find the largest number which divides 438 and 606, leaving remainder 6 in each case.

Q.

If the HCF of 210 and 55 is expressible in the form of 210 ×5 -55y find y

Q. The length, breadth and height of a room are 8m25cm, 6m75cm and 4m50cm respectively. Find the length of the longest rod that can measure the three dimensions of the room exactly.

Q.

Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case.

Q. The length, breadth and height of a room are 8m 50cm, 6m 25cm and 4m 75cm respectively. Find the length of the longest rod that can measure the dimensions of the room exactly.

Q. If two positive integers a and b are written as $a=x^3{y}^{2}andb=x{y}^2$ where x, y are prime numbers, then HCF (a, b) is

1. $xy$
2. $x{y}^2$
3. $x^3{y}^3$
4. $x^2{y}^2$

Q. If p and q are two prime number, then what is their HCF?

Q.

In a school there are two sections $A$ and $B$ there are $32$ students in section A and $36$ students in section $B$. Determine the minimum number of books required for library so that it can be distributed equally among the children.

Q. Find HCF and LCM of 404 and 96 and verify that HCF $\times$ LCM = Product of the two given numbers.

Q.

Find the greatest number which divides 285 and 1245 leaving remainders 9 & 7 respectively .

Q.

Find the largest number which divides 320 and 457, leaving remainders 5 and 7 respectively.

Q.

hey dear i have doubt in word problems of this chapter real numbers

i have to know hole concept of HCF and LCM which is used in word problem.

Q.

Use Euclid's algorithm to find HCF of 1190 and 1445. Express the HCF in the form 1190m+1445n.

Q.

Find the LCM and HCF of $180,144,$and $192$by applying the prime factorization method.

Q.

The exponent of $2$ in the prime factorization of $144,$ is:

1. $4$

2. $5$

3. $6$

4. $3$

Q. The HCF of two numbers is 27 and their LCM is 162. If one of the numbers is 54, what is the other number?

1. 36
2. 9
3. 45
4. 81

Q. If p and q are co-prime numbers, then p² and q² are

(a) coprime
(b) not coprime
(c) even
(d) odd

Q.

HCF of $(2^3\times 3^2\times 5),(2^2\times 3^3\times 5^2)and(2^4\times 3\times 5^3\times 7)$ is

(a) 30 (b) 48 (c) 60 (d)105

Q.

List of coprime numbers between $1$ to $100.$

Q. If the HCF of 144 and 180 is expressed in form of 13p - 3 find value of p

Q. Find the smallest number which when divided by 28 and 32 leaves remainders 8 and 12 respectively.

Q.

15 pastries and 12 biscuit packets have been donated for a school fete. These are to be packed in several smaller identical boxes with the same number of pastries and biscuit packets in each. How many biscuit packets and how many pastries will each box contain?

Q.

Using prime factorisation, find the HCF and LCM of :

(i) 36, 84 (ii) 23, 31 (iii) 96, 404

(iv) 144, 198 (v) 396, 1080 (vi) 1152, 1664

In each case, verify that:

HCF$\times$ LCM = product of given numbers.

Q.

Which of the following is a pair of co-primes ?

(a) (14, 35) (b) (18, 25) (c) (31, 93) (d) (32, 62)