Question

7. Find the largest number which when divides the numbers 34, 83 and 116 leaves 2, 3 and 4 remainders, respectively.​

Answer 1

GOOD AFTERNOON DEAR MATE HAVE A NICE DAY ❤️

ANSWER==>THIS IS A MODEL ANSWER

• The number divides 399,434 and 537 leaving the remainder 8,9 and 10.
• So, that number will divide (399−8),(434−9) and (537−10) completely.
• Now, the greatest number that will divide 391,425 and 527 completely, is the H.C.F. of these numbers.
• 391=17×23
• 425=5×5×17
• 527=17×31

H.C.F. =17

Answer 2

Step-by-step explanation:

Here, we need to find differences between the given numbers. If two numbers give the same remainder when divided by some other number, then their difference must give a remainder of zero when divided by that number. Our numbers here are 91 - 43= 48, 183 91 = 92, 183 - 43140 So we have the set of numbers {48, 92, 140} and we want to know the biggest number that divides all these numbers.

So,

48= 2 x 2 × 2 × 3

922 × 2 × 23

140 = 2 × 2 × 5 × 7

The greatest common divisor of {48, 92, 140} is 4. So, answer is 4.

HOPE IT HELPS ❤️

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