00:01
In this problem, in subpart a, we are asked to find out the greatest common divisor of 132 and 50 and we are asked to write this down as a linear combination.
00:20
So here, let us first consider 132 which gets divided by 50.
00:27
It gives a quotient of 2 and it leaves a remainder of 32.
00:32
So next we consider 50 which when divided by 32 gives a quotient of 1 and leaves a remainder of 18.
00:40
Next we consider 32 which when divided by 18 gives a quotient of 1 and leaves the remainder of 14.
00:48
Next we consider 18 which when divided by 14 gives a quotient of 1 and leaves a remainder of 4.
00:56
Next we consider 14 which when divided by 4 leaves gives a quotient of 3 and leaves a remainder of 2.
01:06
And lastly we consider 4 which when divided by 2 gives a quotient of 2 and leaves a remainder of 0.
01:13
So therefore on dividing by 2 we obtain the remainder to be 0.
01:18
So we have the greatest common divisor to be equal to 2.
01:22
So this is the required answer for the greatest common divisor.
01:25
Now let us express it as a linear combination.
01:28
So moving from this equation, we can write 2 as 14 minus 3 times 4...