Find hcf of 308 and 210 and express it in the form of 310m + 210n and find m and n

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).

Step-by-step 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.