Explanation :
To find the greatest number that can divide both 398 and 436, leaving a remainder of 6 in both cases, we need to subtract 6 from both numbers and find their common factors.
398 - 6 = 392
436 - 6 = 430
Now, we need to find the greatest common factor of 392 and 430.
The factors of 392 are: 1, 2, 4, 7, 8, 14, 28, 49, 56, 98, 196, and 392.
The factors of 430 are: 1, 2, 5, 7, 10, 14, 43, 49, 86, 215, and 430.
From the common factors, the greatest number that divides both 392 and 430, leaving a remainder of 6 in both cases, is 14.
Therefore, 14 is the greatest number that can divide 398 and 436, leaving a remainder of 6 in both cases.