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HCF and LCM
Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case.
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2 Replies
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Here, we need to find differences between the given numbers.
The differences between the given numbers are:
91 – 43 = 48
183 – 91 = 92
183 – 43 = 140
Now, let’s find the Highest Common Factor of these differences (48, 92, 140) is:
48 = 2 * 2 * 2 * 2 * 3
92 = 2 * 2 * 23
140 = 2 * 2 * 5 * 7
HCF = 2 * 2 = 4
Answer: The greatest number that will divide 43,91 and 183 is 4.
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We can start by finding the differences between consecutive pairs of these numbers and find their GCD.<div>
</div><div>The differences are:</div><div>91 – 43 = 48</div><div>183 – 91 = 92</div><div>
</div><div>Now, let’s find the GCD of 48 and 92:</div><div>92 = 48 × 1 + 44</div><div>48 = 44 × 1 + 4</div><div>44 = 4 × 11 + 0</div><div>
</div><div>Since we have obtained a remainder of 0, we can conclude that the GCD of 48 and 92 is 4.</div><div>
</div><div>Therefore, the greatest number that will divide 43, 91, and 183 and leave the same remainder in each case is 4.</div>
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