Hcf value for the given numbers is 14.
The value of m and n is -2 and 3.
The form is 308(-2)+210(3).
Explanation:
To find the hcf:
Step 1: Divide the largest number by the smallest.
308÷210=1+98.
Here 1 is the quotient and 98 is the reminder.
Step 2: Divide the smaller number by the reminder.
210÷98=2+14.
Step 3: Divide the smallest number previous step by its reminder.
98÷14=7+0.
At this step, the remainder is zero, so we stop:
14 is the number we were looking for, the last remainder that is not zero.
∴ 14 is the hcf.
Now we have to find m and n.
To find 308m+210n form,
Write the steps in backwards for the reminder.
For 13 as reminder, 13 = 210-(98×2).
For 98 as reminder 98=308-(210×1).
replace the value of 98,
13=210-((308-(210×1)×2).
13=210-(308×2)+(210×2).
13=(210×3)-(308×2).
13=(-308×2)+(210×3).
since the 308 is given in positive rewrite the form as,
=308(-2)+210(3).
∴ m = -2 and n=3.