Question

What is the greatest number that will divide 139,184 and 424, leaving the remainder 4 in each case??​

Answer 1

Answer:

15

Step-by-step explanation:

This question is easier than it appears. First subtract 4 from each of these numbers as that will be the numbers we seek to find the greatest common divisor for. After this we are left with 135, 180, 420. It can be seen that 20 goes into 180 and 420 evenly, but not 135, and 135 is a multiple of 5. So the next number that should be tried is 15. We can see that 15 divides 135, 180, and 420 with zero remainder. But is it the largest number that will divide all three? Let's focus on 135. A divisor of 135 must be a multiple of 5 if it is to divide 135. You can see that 45 also divides 135. It also divides 180. But it does not divide 420. So we are left to conclude that 15 is the greatest common denominator of 135, 180, and 420, and the greatest common denominator of 139, 184, 424 that leaves a remainder of 4 for each number.

A simpler, more mathematical approach to this problem is to deconstruct each of the three numbers into its unique prime divisor sequence.

135 = 3*3*3*5 , 180 = 2*2*3*3*5, and 420 = 2*2*5*3*7. Now we take only the numbers that all the sequences have in common and write them down to determine the greatest common denominator.

GCD = 3*5 = 15.

hope that helps! :)

Answer 2

15 pls mark brainliest