Highest Common Factors

Q. if d is the hcf of 160 and 24 then find x and y satisfying d =160x plus 24y. also show that x and y are not unique

Q. Find the highest number which divides 24, 30 and 36.

1. 3
2. 6
3. 24
4. 12

Q. if p=3⁴×5², q=2⁴×7×5^m , r=3⁸×2^n and hcf(q, r) = 2³×3^x and HCF(p, q) =5 then find the values of m , n and x respectively.

Q.

Show that the following pairs are co primes $59,97$.

Q.

The HCF of two given numbers is always greater than each of the two number.

1. True
2. False

Q. The sum of two numbers is 105 the HCF of both the numbers is 15 find how many pairs are satisfying the above statement

Q. if d is the HCF of 63 and 81, find x and y satisfying d = 63x + 81y. Also show that x and y are not unique.

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

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

Q.

50 bells B1 , B2 , B3 , .......B50 start ringing together. The bells ring after every 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.....50 sec respectively. Bells $B_{11}$ , $B_{22}$, $B_{33}$ and $B_{44}$ ring together in $2^2.a^1.b^1$ sec. Which of the following is always true about a and b ?

1. LCM of a and b is 22

2. a = 11 and b = 5

3. HCF (a, b) = 1

4. HCF (a, b) = 2

Q. If HCF of two numbers is 1, the two numbers are relatively _________ or __________ . (Fill in the blanks) The options are a)composite, co-prime b)composite, prime c)prime, co-prime d)twin primes, square numbers

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

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

Q. What is composit number ?
What is prime numbers?
Co prime no ?

Q. Find the $LCM\text{and}HCF$ of $120\text{and}45$ by the prime factorization method.

1. LCM = 15
   HCF = 360
2. LCM = 120
   HCF = 15
3. LCM = 360
   HCF = 15

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

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

Q. if d is hcf of 160 and 24 then find x and y satisfying d=160x+24y.Also show that x and y are not unique.

Q. the sum of two numbers in 629 and their hcf is 37. the number of pairs satisfying the above condition is

Q. Find the $LCM\text{and}HCF$ of $120\text{and}45$ by the prime factorization method.

1. LCM = 15
   HCF = 360
2. LCM = 120
   HCF = 15
3. LCM = 360
   HCF = 15

Q.

The LCM of two numbers $525$ and $945$ is $4725$. Find their HCF