Method of Finding H.C.F by Prime Factorization

Q.

Find the least number which when divided by $6,15,18$ leave remainder $5$ in each case.

Q.

Using Euclids division Lemma find the H.C.F of $441,567,693$.

Q.

Three number are in the ratio of 3 : 4 : 5 and their L.C.M. is 2400. What is their H.C.F?

1. 40

Q.

How to find the $LCM$ of $15,20$?

Q. The HCF of 32 and 54 is:

1. 5
2. 2
3. 4
4. 3

Q.

How to find the $LCM$ of $7$ and $9$?

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. Question 6
The numbers 525 and 3000 are both divisible only by 3, 5, 15, 25 and 75. What is the HCF (525, 3000)? Justify your answer.

Q. Visualizing Euclid’s division algorithm, is the values of \(a, b\) and \(c.\)
15 27 

Q.

Use Euclid's algorithm tof find HCF of 1990 and 1445. Express the HCF in the form 1190m + 1445n.

Q.

The HCF of two or more numbers is a factor of their LCM.

Q. If the HCF of 65 and 117 is expressible in the form 65m – 117, then the value of m is:

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

Q. Find the smallest number which when increased by 17 is exactly divisible by both 520 and 468.

1. 4663
2. 2244
3. 7893
4. 4416

Q.

Find the HCF of 24, 32 and 36.

1. 4

2. 2

3. 3

4. 1

Q.

If $a=2^3\times 3^4\times 7^2$and $b=2^3\times 3^2\times 5^3,$ then which of the following is true?

1. $HCF=2^3\times 3^2;LCM=2^3\times 3^4\times 5^3\times 7^2$
2. $HCF=2^3\times 3^2;LCM=2^3\times 3^2\times 5^2\times 7^3$
3. $HCF=2^3\times 3^2;LCM=2^3\times 3^2\times 5^3\times 7^3$
4. $LCM=2^2\times 3^2;HCF=2^3\times 3^3\times 5^3\times 7^2$

Q. What is the HCF of two consecutive natural numbers p and q?

1. 1
2. q
3. p
4. pq

Q.

If $a=2^3\times 3^2\times 5$ and $b=2^4\times 3\times 7^2$, then which of the following is true?

1. HCF = $2^3\times 3^2\times 5\times 7$
   LCM = $2^7\times 3^3\times 5\times 7^2$

2. HCF = $2\times 3\times 5\times 7$
   LCM = $2^2\times 3^2\times 5\times 7^2$

3. HCF = $2^3\times 3^2$
   LCM = $2^4\times 3^2\times 5\times 7^2$

4. HCF = $2^3\times 3$
   LCM = $2^4\times 3^2\times 5\times 7^2$

Q. The H.C.F. of 420 and 130 is .

1. 11
2. 13
3. 10

Q. numbers are the numbers whose HCF is 1.

1. Co-prime
2. Composite
3. Natural

Q. The HCF of 296 and 324 is .

1. 9
2. 8
3. 4

Q.

Use Euclid's algorithm tof find HCF of 1990 and 1445. Express the HCF in the form 1190m + 1445n.

Q. A rectangular courtyard 3.78 metres long and 5.25 metres wide is to be paved exactly with square tiles, all of the same size. The longest side of the tile which could be used for the purpose is (n $\times$ 3) cm. Find n.

1. 7
2. 8
3. 9
4. 6

Q.

Find the HCF of 360 and 18144 by prime factorization.

1. $2\times 3\times 5\times 7$

2. $2^3\times 3^4$

3. $2^5\times 3^2$

4. $2^3\times 3^2$

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.

Question 4
If the HCF of 65 and 117 is expressible in the form 65m - 117, then the value of m is

A) 4
B) 2
C) 1
D) 3

Q. The HCF of 468 and 222 can be expressed as 468x + 222y, where x and y are integers. Find the value of x + y.

1. 8
2. 10
3. -26
4. -8