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.

Explanation:

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

Therefore, the value of m is 2.