HCF Calculation for 85 and 153
First, we need to find the Highest Common Factor (HCF) of 85 and 153. We can use the Euclidean Algorithm.
- Divide 153 by 85: $153 = 1 \times 85 + 68$
- Divide 85 by the remainder 68: $85 = 1 \times 68 + 17$
- Divide 68 by the remainder 17: $68 = 4 \times 17 + 0$
The last non-zero remainder is 17. Therefore, the HCF of 85 and 153 is 17.
Solving for x
The problem states that the HCF can be expressed in the form $85x - 153$. We found the HCF to be 17.
We set up the equation:
$17 = 85x - 153$Now, we solve for x:
- Add 153 to both sides of the equation: $17 + 153 = 85x$ $170 = 85x$
- Divide both sides by 85: $x = \frac{170}{85}$ $x = 2$
Thus, the value of x is 2.
Similar Questions
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Important Questions from LCM and HCF
The HCF and LCM of two numbers are 12 and 72, respectively. If the ratio of the two numbers is 2 ∶ 3, then the larger of the two numbers is:
Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case.
Joseph visits the club on every 5 th day, Harsh visits on every 24 th day, while Sumit visits on every 9 th day. If all three of them met at the club on a Sunday, then on which day will all three of them meet again?
What is the least number which when divided by 12,20 and 24 leaves in each case a remainder of 8?
Which of the following is a pair of co-primes?
