Question

Find the greatest number which when divides 590, 908 and 1014 leaves same remainder each time

Answer 1

Reminder didn't give so

1014 - 908 = 106

1014 - 590 = 424

908 - 590 = 318

HCF of 106, 424, 318 = 106

106 is the greatest number

Answer 2

The greatest number which when divides 590, 908 and 1014 leaves same remainder each time is 106.

Given: 590, 908 and 1014

To find: Find the greatest number which when divides 590, 908 and 1014 leaves same remainder each time.

Step 1: Subtract the numbers.

Remainder is not given.

In this case find the difference of two-2 numbers.

$908 - 590 =318 \\ 1014 - 590 =424 \\ 1014 - 908 = 106$

Step 2: Do prime factors of numbers obtained in step 1.

$318 = 2 \times 3 \times 53$

$424 = 2 \times 2 \times 2 \times 53$

$106 = 2 \times 53$

Step 3: Find HCF of 318,424 and 106.

From prime factors of the numbers, find the HCF of these numbers.

$HCF(318, 424, 106) = 2 \times 53$

or

$HCF(318, 424, 106) = 106$

Thus,

106 is the greatest number which when divides 590, 908 and 1014 leaves same remainder each time.

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