Find the G.C.D of 595 and 252 and express it in the form 595m+252n.i have found the G.C.D i.e 7 now i would like to know how do you find m and n. Can someone please explain the steps?

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to write the factored form of the number 595 such that:

`595 = 1*5*119`

Hence, the divisors of 595 are `{1;5;119;595}`

You need to write the factored form of the number 252 such that:

`252 = 1*2^2*3^2*7`

Hence, the divisors of 252 are `{1;2;3;4;6;7;9;12;14;18;21;63;252}`

You need to notice that the sets of divisors of 595 and 252 share in common only the number 1.

Hence, evaluating the greatest common divisor of 252 and 595 yields that `G.C.D = 1`.

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