How do you express the HCF of 85 and 153 in terms of 85m + 153, and what is the value of m?

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To find the value of m expressed in the equation HCF = 85m + 153, we first need to determine the HCF (Highest Common Factor) of the numbers 85 and 153.

First, we factor both numbers:

  • 85: The factors of 85 are 1, 5, 17, 85
  • 153: The factors of 153 are 1, 3, 9, 17, 51, 153

Next, we find the common factors of these two sets:

  • The common factors are 1, and 17 (as it is the only number present in both lists).

Thus, the HCF of 85 and 153 is 17.

Now, we need to express this HCF in the form 85m + 153. Setting up the equation:

 
    85m + 153 = 17

To isolate m, we rearrange the equation:

 
    85m = 17 - 153 
    85m = -136

Next, we solve for m by dividing both sides by 85:

 
    m = -136 / 85 
    m = -1.6

Therefore, the value of m is -1.6.

In summary, the HCF of 85 and 153 expressed in the form 85m + 153 has the value of:

m = -1.6.

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