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Use euclid division algorithm to find …

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Use euclid division algorithm to find HCF of 1190 and 1445 and express the HCF in the form 1190a + 1445b and also find a and b .

    • Posted by Agni Shikha 6 years, 4 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Sia ? 6 years, 4 months ago

    Here we have to find HCF of 1190 and 1445 and express the HCF in the form 1190m + 1445n.
    1445 = 1190 × 1 + 255
    1190 = 255 × 4 + 170
    255 = 170 × 1 + 85
    170 = 85 × 2 + 0
    So, now the remainder is 0, then HCF is 85
    Now,
    85 = 255 - 170
    = (1445 - 1190) - (1190 - 255 × 4)
    = 1445 - 1190 - 1190 + 255 × 4
    = 1445 - 1190 × 2 + (1445 - 1190) × 4
    = 1445 - 1190 × 2 + 1445 × 4 - 1190 × 4
    = 1445 × 5 - 1190 × 6
    = 1190 × (- 6) + 1445 × 5
    = 1190m + 1445n , where m = - 6 and n = 5

    0Thank You

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