Find the largest number which devides438&606leaving remainder 6in each...
We have to find HCF OF (438-6) and (606-6)i.e 432 and 600here 600>432 600 = 432x1+168 432 = 168x2+96 168 = 96x1+72 96 = 72x1+2472 = 24x3+0 so HCF is 24
Find the largest number which devides438&606leaving remainder 6in each...
Identifying the Problem:
To determine whether to find the Least Common Multiple (LCM) or Highest Common Factor (HCF) in a problem like this, we need to analyze the given numbers and the conditions provided. In this case, we are looking for the largest number that divides 438 and 606, leaving a remainder of 6 in each case.
Solution Approach:
1. Start by finding the difference between 438 and 606:
606 - 438 = 168
2. Since the remainder in both cases is the same (6), we need to find a number that divides both 168 and the original numbers (438 and 606).
3. Now, we need to find the divisors of 168 that also divide 438 and 606.
Factors of 168: 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168
4. Among the factors of 168, we need to find the largest number that leaves a remainder of 6 when dividing 438 and 606.
Determining the Largest Number:
From the factors of 168, we need to find the largest number that divides both 438 and 606 while leaving a remainder of 6.
- 84 is the largest number that satisfies these conditions.
Therefore, the largest number that divides 438 and 606, leaving a remainder of 6 in each case, is 84.
By following these steps, we can approach the problem systematically and determine whether to find LCM or HCF based on the given conditions.
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