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If q is the ICF of 56 and 72, Find a and b satistying q - 50a + 72b |
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Answer» BY APPLYING EUCLID's DIVISION LEMMA TO 56 AND 72 : 72 = 56 × 1 +16 ------------ (1) 56 = 16 × 3 + 8 ------------ (2) 16 = 8 × 2 + 0 -------------- (3) THEREFORE HCF OF 56 AND 72 = 8 FROM (2) -- 8 = 56 - 16 ×3 8 = 56 - (72-56×1) ×3 (from 1)8 = 56 - 3 × 72 + 56 × 3 8 = 56 × 4 + (-3) × 72 therefore , x = 4 and y = -3 Now, 8 = 56 × 4 + (-3) × 72 8 = 56 × 4 + (-3) × 72 - 56 × 72 + 56 × 72 8 = 56 × 4 -56 × 72 + (-3) × 72 + 56 ×72 8 = 56 × (4-72) + {(-3) + 56} × 72 8 = 56 × (-68) + (53) × 72 therefore x = -68 and y = 53 |
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