Find the largest number which divides 436, 530, 624 and 718, leaving 13 as the remainder in each case.

Correct option is C

Given:
Numbers = 436, 530, 624, 718
Remainder = 13
Formula Used:
Largest number that divides the given numbers leaving the same remainder = HCF of the differences of the numbers
Solution:
Numbers after subtracting the remainder (13):
436 - 13 = 423
530 - 13 = 517
624 - 13 = 611
718 - 13 = 705
Differences between these to find HCF
517 - 423 = 94
611- 517 = 94
705 - 611 = 94
Find the HCF of these differences (94):
Factors of 94 = 1, 2, 47, 94
The largest factor = 47 
Alternate Solution:
Numbers after subtracting the remainder (13):
436 - 13 = 423
530 - 13 = 517
624 - 13 = 611
718 - 13 = 705 
Find HCF by using prime factorization: 
• 423 = 3 × 3 × 47 or 3² × 47
• 517 = 11 × 47
• 611 = 13 × 47
• 705= 3 × 5 × 47
The largest factor = 47