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In finding the HCF of two numbers by division method, the last divisor is 49 and the quotients are 17, 3, 2. Find the two numbers.
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- 243 and 4929
- 343 and 5929
- 334 and 5992
- None of these
Correct Option: B
Here, the last divisor = 49 and quotient = 2
or, Symbolically the process of finding the HCF by division method can be shown in this way.
the dividend (c) = 49 × 2 = 98
Now, divisor = 98,
quotient = 3 and remainder = 49
∴ Dividend (a) = 98 × 3 + 49 = 294 + 49 = 343
Again, divisor = 343, quotient = 17 and remainder = 98
∴ Dividend (b) = 343 × 17 + 98 = 5831+ 98 = 5929
Thus, two numbers are 343 and 5929.
Second method to solve this question :
| a | b | c | 49 | |
| Remainders → | 17 | 3 | 2 |
Let two numbers are a and b.
c = 2 × 49 = 98
b = 3c + 49 = 3 × 98 + 49 = 343
a = 17b + c = 17 × 343 + 98 = 5929
