If the HCF of 85 and 153 is expressible in the form of 85m -153; then find the value of m.
HCF (Highest Common Factor) of two numbers is the largest possible number which divides the two numbers exactly without leaving any remainder.
Answer: If the HCF of 85 and 153 is expressible in the form of 85m -153, the value of m is 2.
HCF of 85 and 153 is the highest number that divides 85 and 153 exactly leaving the remainder 0.
We are using the division method to find the HCF of 85 and 153.
The steps to find the HCF(85, 153) by long division are mentioned below.
- Step 1: Divide 153 by 85 and check the remainder. We get the remainder as 68.
- Step 2: Make the remainder of the above step 68 as the divisor and the divisor of the above step 85 as the dividend and perform the long division again.
- Step 3: Continue till you get the remainder as 0 and the last divisor is the HCF of 85 and 153.
The highest common factor of 85 and 153 is 17.
Now equate 85m - 153 to 17 and simplify to find the value of m.
85m - 153 = 17
85m = 153 + 17
85m = 170
m = 170/85
m = 2