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use Euclid's algorithms to find HCF …

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use Euclid's algorithms to find HCF of 1190 and 1445 . Express the HCF in the form of 1190m+1445n

    • Posted by A Mariyappan 5 years, 1 month ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Yogita Ingle 5 years, 1 month ago

    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

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