Question

If d is the Highest Common Factor of 32 and 60, find x and y satisfying d = 32x + 60 y. ​

Answer 1

Answer:

x = 2 and y = -1.

Step-by-step explanation:

60 > 32

60  =  32(1) + 28 ----(1)

32  =  28(1) + 4 ----(2)

28  =  4(7) + 0 ----(3)

Hence the H.C.F of 60 and 32 is 4.

d = 4

d = 32x + 60y  

4  =  32 x + 60 y

From (2), let us solve for 4

4  =  32 - 28(1) ---(4)

From (1), let us solve for 28

28  =  60 - 32(1)---(5)

By applying the value of 28 from (5) into (4), we get

4  =  32 - (60 - 32(1)) ×1

4  =  32 - 60× 1 + 32 (1) × 1

4  =  32 + 32 (1) - 60 × 1  

4  =  32(1 + 1) - 60 × 1  

4  =  32(2) + 60 (-1)  

Instead of x, we have 2 and instead of y, we have -1.

Hence x = 2 and y = -1.

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