Find the greatest number that divides 165, 246, 300, and 408 to leave

1.	Find the greatest number that divides 165, 246, 300, and 408 to leave 3 remainders in each case.1. 212. 233. 274. 29
Answer» Correct Answer - Option 3 : 27 Given: The number is 165, 246, 300, and 408 The remainder is 3 in each case Concept: First, subtract 3 from each number then find the HCF of the obtained number after subtracting. Calculation: 165 - 3 = 162, 246 - 3 = 243, 300 - 3 = 297, 408 - 3 = 405 Now, find the HCF of 162, 243, 297, and 405 162 = 27 × 6 243 = 27 × 9 297 = 27 × 11 405 = 27 × 15 Now, we see that nothing is common among (6, 9, 11, 15) so highest common factor is 27. ∴ The required greatest number is 27.

Find the greatest number that divides 165, 246, 300, and 408 to leave 3 remainders in each case.1. 212. 233. 274. 29

Answer» Correct Answer - Option 3 : 27

Given:

The number is 165, 246, 300, and 408

The remainder is 3 in each case

Concept:

First, subtract 3 from each number then find the HCF of the obtained number after subtracting.

Calculation:

165 - 3 = 162, 246 - 3 = 243, 300 - 3 = 297, 408 - 3 = 405

Now, find the HCF of 162, 243, 297, and 405

162 = 27 × 6

243 = 27 × 9

297 = 27 × 11

405 = 27 × 15

Now, we see that nothing is common among (6, 9, 11, 15) so highest common factor is 27.

∴ The required greatest number is 27.

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