Question

Find HCF of 592 and 252 and express it in linear combination of 592 and 252.

Answer 1

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Answer 2

Answer:

4 = 592m + 252n , where m = -20 and n = 47

Step-by-step explanation:

592 = 252 × 2 + 88

252 = 88 × 2 + 76

88 = 76 × 1 + 12

76 = 12 × 6 + 4

12 = 4 × 3 + 0

Hence, H.C.F = 4

Now, 4 = 76 - 12 × 6

4 = 76 - (88 - 76 ) × 6

4 = 76 × 7 - 88 × 6

4 =  (252 - 88 × 2) × 7 - 88 × 6

4 = 252 × 7 - 88 × 20

4 = 252 × 7 - (592 - 252 × 2) × 20

4 = 252 × 47 - 592 × 20

⇒ 4 = 592m + 252n

where m = -20 and n = 47

Hence, This is the required linear combination form.