The sum of two numbers is 462 and their highest common factor is 22. What is the minimum number of pairs that satisfy these conditions?
বিকল্পসমূহ (নিজের উত্তর যাচাই করতে ক্লিক করুন):
সঠিক উত্তর
2 (6)
বিস্তারিত ব্যাখ্যা ও বিশ্লেষণ:
Let the two numbers be 22a and 22b where a and b are co-primes.
=> 22a + 22b = 462
=> a + b = 462/22 = 21
Combinations of (a,b) are as follows:
(1,20), (2,19),(3,18),(4,17),(5,16),(6,15),(7,14),(8,13),(9,12),(10,11)
However, (3,18), (6,15),(7,14),(9,12) are not admissible as the pairs are NOT co-primes.
Thus, 6 combinations are possible. (22,440) (44,418) (88,374) (110,352) (176,286) (220,242)
