Question

Find the HCF of 143 and 481. Also find two integers m and n such that HCF (143,481)= 143m + 481n

Answer 1

Step-by-step explanation:

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H.C.F. of 143 and 481

481 = 143×3+52

143 = 52×2+39

52 = 39×1+13

39 = 13×3+0

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Answer 2

Concept

Highest common factor is also called as HCF. it is defines as highest possible number which divides both the given numbers.

Given:

Two numbers 143 and 481

Find

HCF of the two given numbers 143 and 481.

Solution

• HCF can simply be calculated by determining the factors of the two numbers.

• 143 can be written as 11 × 13 , 481 can be written as 37 × 13.

• By observing the factors HCF is found to be  =13.

• The given HCF 143m + 481n

            So equating both HCF, we get as

                       143 m + 481n = 13,

             37m × 13 + 37n × 13 = 13,

                          Taking 13 common on both sides,

                 ⇒ 13 (11m + 37n ) = 13

                      ⇒ (11m + 37n ) = 1     ---(i)

Now using trail and error method  the above equation will be satisfied by (-10,3).

Hence HCF of 143 and 481 is 13 , m and n are  -10 and 3 respectively.

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