Use Euclid’s algorithm to find the HCF of 1190 and 1445. Express the HCF in the form 1190m+1445n.​

2 thoughts on “Use Euclid’s algorithm to find the HCF of 1190 and 1445. Express the HCF in the form 1190m+1445n.​”

1. Answer:

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   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

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2. Solution:

   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

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