Advertisements
Advertisements
Question
If the HCF of 65 and 117 is expressible in the form 65m – 117, then the value of m is ______.
Options
4
2
1
3
Advertisements
Solution
If the HCF of 65 and 117 is expressible in the form 65m – 117, then the value of m is 2.
Explanation:
Let us find the HCF of 65 and 117,
117 = 1 × 65 + 52
65 = 1 × 52 + 13
52 = 4 × 13 + 0
Hence, we get the HCF of 65 and 117 = 13.
65m – 117 = 13
65m = 117 + 13 = 130
∴ m = `130/65` = 2
APPEARS IN
RELATED QUESTIONS
Consider the number 12n where n is a natural number. Check whether there is any value of n ∈ N for which 12n ends with the digital zero.
Find the LCM and HCF of the following integers by applying the prime factorisation method.
12, 15 and 21
Determine the prime factorisation of each of the following positive integer:
58500
Find the LCM and HCF of the following pair of integers and verify that LCM × HCF = Product of the two numbers.
26 and 91
State Fundamental Theorem of Arithmetic.
Express the number as a product of its prime factor:
3825
For what value of natural number n, 4n can end with the digit 6?
Find the least positive value of x such that 89 ≡ (x + 3) (mod 4)
Three farmers have 490 kg, 588 kg and 882 kg of wheat respectively. Find the maximum capacity of a bag so that the wheat can be packed in exact number of bags.
For some integer p, every odd integer is of the form ______.
The ratio of LCM and HCF of the least composite and the least prime numbers is ______.
If LCM(x, 18) = 36 and HCF(x, 18) = 2, then x is ______.
If two positive integers p and q can be expressed as p = ab2 and q = a3b; a, b being prime numbers, then LCM (p, q) is ______.
The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is ______.
On a morning walk, three persons step off together and their steps measure 40 cm, 42 cm and 45 cm, respectively. What is the minimum distance each should walk so that each can cover the same distance in complete steps?
Let a and b be two positive integers such that a = p3q4 and b = p2q3, where p and q are prime numbers. If HCF (a, b) = pmqn and LCM (a, b) = prqs, then (m + n)(r + s) = ______.
Two numbers are in the ratio 2 : 3 and their LCM is 180. What is the HCF of these numbers?
Assertion (A): The HCF of two numbers is 5 and their product is 150. Then their LCM is 40.
Reason(R): For any two positive integers a and b, HCF (a, b) × LCM (a, b) = a × b.
If HCF (72, 120) = 24, then LCM (72, 120) is ______.
The prime factorisation of the number 2304 is ______.
