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
Check whether 6n can end with the digit 0 for any natural number n.
Find HCF and LCM of 404 and 96 and verify that HCF × LCM = Product of the two given numbers.
State fundamental theorem of arithmetic?
Determine the prime factorisation of each of the following positive integer:
20570
Find the LCM and HCF of the following pair of integers and verify that LCM × HCF = Product of the two numbers.
26 and 91
If the prime factorization of a natural number n is 23 ✕ 32 ✕ 52 ✕ 7, write the number of consecutive zeros in n.
Find the LCM and HCF of the following pair of integers and verify that LCM × HCF = product of the two numbers.
510 and 92
If m, n are natural numbers, for what values of m, does 2n × 5m ends in 5?
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 ______.
When a number is divided by 7, its remainder is always ______.
The ratio of LCM and HCF of the least composite and the least prime numbers is ______.
For some integer q, every odd integer is of the form ______.
The largest number which divides 70 and 125, leaving remainders 5 and 8, respectively, is ______.
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) = ______.
Show the 6n cannot end with digit 0 for any natural number 'n'.
(HCF × LCM) for the numbers 70 and 40 is ______.
If two positive integers a and b are written as a = x3y2 and b = xy3, where x, y are prime numbers, then the result obtained by dividing the product of the positive integers by the LCM (a, b) is ______.
The HCF of two numbers 65 and 104 is 13. If LCM of 65 and 104 is 40x, then the value of x is ______.
