Question

What is the greatest number, by which when 8954, 9806 and 11297 are divided, the remainder in each case is the same?

• A. 125
• B. 213
• C. 230
• D. 222

Answer 1

Answer:

B. 213

To find the greatest number that leaves the same remainder when dividing three given numbers, you need to find the Highest Common Factor (HCF) of the absolute differences between the numbers.

The numbers are:

$A = 8954$

$B = 9806$

$C = 11297$

## Step 1: Find the differences between the numbers

* $B - A = 9806 - 8954 = 852$

* $C - B = 11297 - 9806 = 1491$

* $C - A = 11297 - 8954 = 2343$

## Step 2: Find the HCF of 852, 1491, and 2343

Let's find the HCF of the two smaller differences, 852 and 1491, using the division method:

1. Divide 1491 by 852:

$1491 = 852 \times 1 + 639$ (Remainder = 639)

2. Now divide 852 by 639:

$852 = 639 \times 1 + 213$ (Remainder = 213)

3. Now divide 639 by 213:

$639 = 213 \times 3 + 0$ (Remainder = 0)

The HCF of 852 and 1491 is 213.

The greatest number is 213.