If the HCF of 408 and 1032 is Expressible in the Form 1032m − 408 × 5, Find m

Video Explanation

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Solution

Question: If the HCF of 408 and 1032 is expressible in the form 1032m − 408 × 5, find the value of m.

Step 1: Find the HCF of 408 and 1032

Using Euclid’s division algorithm:

1032 = 408 × 2 + 216

408 = 216 × 1 + 192

216 = 192 × 1 + 24

192 = 24 × 8 + 0

Since the remainder is zero,

∴ HCF (408, 1032) = 24

Step 2: Use the Given Expression

Given that:

HCF = 1032m − 408 × 5

Substitute HCF = 24

24 = 1032m − 2040

1032m = 2064

m = 2

Final Answer

∴ The value of m = 2.

Conclusion

Thus, by finding the HCF using Euclid’s division algorithm and comparing it with the given linear form, we get the value of m = 2.