Find the largest positive integer that will divide 398,436 and 542 leaving remainders 7,11 and 15 respectively.
Know your College Admission Chances Based on your Rank/Percentile, Category and Home State.
Get your JEE Main Personalised Report with Top Predicted Colleges in JoSA
It is given that on dividing 398 by the required number, there is a remainder of 7.
This means that 398 − 7 = 391 is exactly divisible by the required number. In other words required number is a factor of 391.
Similarly, required positive integer is a factor of 436 − 11 = 425 and 542 − 15 = 527.
Clearly, required number is the HCF of 391,425 and 527.
Using the factor theorem the prime factorizations of 391,425 and 527 are as follows:
391 = 17 × 23, 425 = 52 × 17 and 527 = 17 × 31
∴ HCF of 391,425 and 527 is 17
Hence, required number = 17