Question

The greatest number that will divide 2930 and 3250, and will leave remainder 7 and 11 respectively is
A. 59 B. 79 C. 37 D. 53

Answer 1

Hint: Here, we will use the concept of H.C.F. (Highest common factor). We have to find the highest common factor of (2930 – 7) and (3250 – 11) i.e. 2923 and 3239. Using prime factorization, find the HCF of these two numbers to get the result.

Complete step-by-step answer:
Let x be the number that will divide 2930 and 3250 and will leave remainder 7 and 11. That means there will be no remainders if x divides (2930 – 7) and (3250 – 11) i.e. 2923 and 3239.
Thus by using Prime Factorization Method
2923 = 37 × 79 and 3239 = 41 × 79
In 2923 and 3239 the common factor is 79.
Thus HCF (2923, 3239) = 79
[Highest common factor of two numbers is the highest factor common in both numbers when two numbers are represented in terms of its prime factorization]
Verification: If we divide 2930 by 79 we get quotient = 37 and remainder = 7.
If we divide 3250 by 79 we get quotient = 41 and remainder = 11.

Thus the greatest number that will divide 2930 and 3250 to leave 7 and 11 as remainder is 79.

Note: In these types of questions, obtain the dividend using the conditions given in question, so that there is no remainder left. Do not factorize the numbers without addition or subtraction according to the given statement. Be careful while choosing the concept used in the solution and be specific about when to choose HCF or LCM. Lastly, always verify the result obtained.