It is given that required number which divides 245 and 1029, the remainder is 5 in each case.
⇒ 245 - 5 = 240 and 1029 - 5 = 1024 are completely divisible by the required number.
Since, it is given that the required number is the largest number.
Therefore, it is the HCF of 240 and 1024.
Now, finding HCF by Euclid’s division algorithm.
Given integers are 240 and 1024.
Clearly 1024 > 240.
Therefore, it is the HCF of 240 and 1024 and 240, we get
II. Since, the remainder 64 ≠ 0, we apply division lemma to get
III. We consider the new divisor 64 and remainder 48 and apply division lemma to get
IV. We consider the new divisor 48 and new remainder 16 to get
V. The remainder at this step is zero. So, the divisor at this stage or the remainder at the previous stage i.e., 16 is the HCF of 245 and 1029.
