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The largest number which divides 245 and 1029 leaving remainder 5 in each case is
- a)4
- b)8
- c)12
- d)16
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
The largest number which divides 245 and 1029 leaving remainder 5 in e...
When 245 and 1029 are divided by the required number then there is left 5 as remainder. It means that 245 - 5 = 240 and 1029 - 5 = 1024 will be completely divisible by the required number.
Now we determine the HCF of 240 and 1024 by Euclid's Algorithm.
1024 = 240 x 4 + 64
240 = 64 x 3 + 48
64 = 48 x 1 + 16
48 = 16 x 3 + 0
Since remainder comes zero with last divisor 16,
required number = 16
Now we determine the HCF of 240 and 1024 by Euclid's Algorithm.
1024 = 240 x 4 + 64
240 = 64 x 3 + 48
64 = 48 x 1 + 16
48 = 16 x 3 + 0
Since remainder comes zero with last divisor 16,
required number = 16
Most Upvoted Answer
The largest number which divides 245 and 1029 leaving remainder 5 in e...
Hey,
We will have to find the HCF of these numbers which leaves 5 in each case.
Therefore the numbers will be : 245-5=240 and 1029-5=1024
We can solve using prime factorization or Euclid's division lemma
Since I cant show you the Euclids division lemma, I will just write the steps involved:
1024 = 240*4+64
240 = 64*2+48
64 = 48*1+16
48 = 16*3+0
Therefore the HCF is 16. So option D is correct.
Or of by prime factorization:
1024= 2^10
240 = 2^4 *3 * 5
HCF= 2^4= 16... So option D is correct.
Hope this helps you!
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Community Answer
The largest number which divides 245 and 1029 leaving remainder 5 in e...
When 245 and 1029 are divided by the required number then there is left 5 as remainder. It means that 245 - 5 = 240 and 1029 - 5 = 1024 will be completely divisible by the required number.
Now we determine the HCF of 240 and 1024 by Euclid's Algorithm.
1024 = 240 x 4 + 64
240 = 64 x 3 + 48
64 = 48 x 1 + 16
48 = 16 x 3 + 0
Since remainder comes zero with last divisor 16,
required number = 16
Now we determine the HCF of 240 and 1024 by Euclid's Algorithm.
1024 = 240 x 4 + 64
240 = 64 x 3 + 48
64 = 48 x 1 + 16
48 = 16 x 3 + 0
Since remainder comes zero with last divisor 16,
required number = 16
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The largest number which divides 245 and 1029 leaving remainder 5 in each case isa)4b)8c)12d)16Correct answer is option 'D'. Can you explain this answer?
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