HCF AND LCM-02

Question: Find the greatest number which is such that when 76, 151 and 226 are divided by it, the remainders are all alike. Find also the common remainder. [वह सबसे बड़ी संख्या निकालें, जिससे 76, 151 तथा 226 को भाग देने पर समान शेषफल बचते हैं. कॉमन शेषफल भी बताएं.]     [Ans. (c) 75, 1]       

(a) 57, 2    (b) 75, 2     (c) 75, 1     (d) 57, 1    (e) none of these

Solution:

Detailed Explanation:

Concept: If remainders are given, then they are subtracted from the given numbers, and then HCF is determined. But, it remainders are not given, then they must be equal. When the difference of two numbers is taken, then remainders are cancelled and it becomes divisible. So, we find the HCF of the differences between the numbers.

Therefore, HCF of (151-76), (226-151) and (226-76)

                                 = HCF of 75, 75 and 150 = 75

                                  Common remainder = 1 Ans.