Question

Find the greatest nuber which will divide 12288,28421, and 44333 so as to leave the same remainder in each cse.

Answer 1

Answer:

1

one is the only greatest common factor of these nos.. as to leave the same remainder in each case

Step-by-step explanation:

Answer 2

221 is the greatest number that divides 12288,28421, and 44333 leaving the same remainder.

Given:

Three numbers are 12288,28421 and 44333.

To Find:

The greatest number divides 12288, 28421, and 44333 with the same remainder.

Solution:

Let r be the remainder and X be the greatest number that divides 12288, 28421, and 44333 with the same remainder r.

⇒ (12288-r),(28421-r), and (44333-r) are exactly divided by the number X.

Since, We know that When two numbers are divided by the same number then, the difference between the two numbers is also divided by the same number.

∴ The difference between first two numbers = 28421-r-12288+r =16133.

Also, The difference between the last two numbers = 44333-r-28421+r=15912

⇒ 16133 and 15912 are also divisible by X.

16133 = 13 * 17 * 73

15912 = 2³ * 3² * 13 * 17

HCF of 16133 and 15912 = 13 *17 =221.

Therefore, 221 is the greatest number that divides 12288,28421, and 44333 leaving the same remainder.

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