To find the value of m such that the highest common factor (HCF) of 85 and 153 can be expressed in the form of 85m + 153, we first need to calculate the HCF of 85 and 153.
We can use the prime factorization method to do this:
- 85 can be factored into 5 and 17, so: 85 = 5 × 17.
- 153 can be factored into 3 and 51 (where 51 can further be factored into 3 and 17), so: 153 = 3 × 3 × 17 = 3² × 17.
The common factor between the two numbers is 17. Thus, the HCF of 85 and 153 is:
HCF = 17
Next, we want to express HCF in the form of 85m + 153:
17 = 85m + 153
Now, we can rearrange this equation to find m:
- Subtract 153 from both sides:
- 85m = 17 – 153
- 85m = -136
- Now, divide both sides by 85:
- m = -136 / 85
- m = -1.6
Thus, we conclude that the value of m is:
m = -1.6
This means the equation holds true, and we have determined the value of m accordingly.