Answer:
388
Step-by-step explanation:
<u>Definition from Wikipedia</u>
In mathematics, the greatest common divisor (GCD) of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers. For two integers x, y, the greatest common divisor of x and y is denoted as gcd(x,y) . For example, the GCD of 8 and 12 is 4, that is, gcd(8,4)=4 (https://en.wikipedia.org/wiki/Greatest_common_divisor)
<u>Methodology to find greatest common denominator(factor) for 2 numbers</u>
- Write down the divisors of both numbers
- Collect the common divisors of both terms
- Choose the largest divisor from the above terms
- The divisors of 24 are 1, 2, 3, 4, 6, 8, 12, 24
- Since the number is less than 400, it must be 4 x D where D < 100
- Let's try 4 x 99 = 396. Divisors are 1, 2, 3, 4, 6, 9, 11, 12, 18, 22, 33, 36, 44, 66, 99, 132, 198, 396. gcd(24, 396) = 12.
- Try D = 98 ==> 4 x 98 = 392 with divisors 1, 2, 4, 7, 8, 14, 28, 49, 56, 98, 196, 392. gcd(24, 392) = 8
- Try D = 97 ==> 4 x 97 = 388. Divisors of 388 are 1, 2, 4, 97, 194, 388 gcd(4, 388) = 4
Note that even though I have listed all divisors of the higher number, you don't have to compute all divisors. You can stop figuring out the divisors once the larger number is divisible by the number that is higher than 4 but slosest to i. For example, in the case of 396, I would stop computing as soon as I found it is divisible by 6
