Find the greatest number that divides 215, 245 and 365 leaving a remainder of 5 in each case. (With Explanation)
Answers
Answer:
The two numbers are 245 and 1029. You want the largest number that divides the two numbers leaving a remainder of 5 in each case.
First subtract 5 from 245 and 1029 to get
245 - 5 = 240.
1029 - 5 = 1024,
Next find the HCF of 240 and 1024. To do that find the prime factors of the two numbers:
240 = 2x2x2x2x3x5 = 2^4x3x5
1024 = 2x2x2x2x2x2x2x2x2x2 = 2^10
Thus the HCF = 2^4 = 16. So the answer is 16.
Check: 245/16 = 30 + 5 remainder
1029/16 = 64+ 5 remainder
Correct.
Answer:
The final answer is 10.
Step-by-step explanation:
We have three numbers 215 , 245 and 365. First we need to find the HCF of the three numbers. The HCF of these numbers is the greatest number which divides these numbers equally.
HCF = 5
5 divides each of the three numbers such that they leave a remainder of zero. But we also know that we need to find a number such that it divides the numbers and leaves a remainder of 5.
Essentially we get a remainder zero dividing with 5, To get a remainder 5 we simply add 5 to it.
We get a number = 10. This will give us a remainder of 5 in every case.
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