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

By BYJU'S Exam Prep

Updated on: September 25th, 2023

To find: the value of ‘m’ for HCF of 408 and 1032 which is expressible in the form of 1032 m − 408 × 5.

To solve this, use the Euclid’s division algorithm,

1032 = 408 × 2 + 216

408 = 216 × 1 + 192

216 = 192 × 1 + 24

192 = 24 × 8 + 0

The HCF of the given numbers is 24 because the remainder is zero.

Now, find the value of ‘m’.

1032m − 408 × 5 = HCF of the number

1032m − 408 × 5 = 24

1032m − 2040 = 24

1032m = 24 + 2040

1032m = 2064

m = 2064 ÷ 1032

m = 2

Therefore, the value of ‘m’ for HCF of 408 and 1032 in the form of 1032 m − 408 × 5 is 2.

Value of ‘m’ for HCF of 408 and 1032 in form of 1032 m − 408 × 5

Using Euclid’s division algorithm the value of ‘m’ for HCF of 408 and 1032 which is expressible in the form of 1032 m − 408 × 5 can be easily determined. Let us understand what Euclid’s division algorithm is.

Using Euclid’s division lemma, the Euclid’s division algorithm can be used to determine the HCF of two numbers. It says that if there are any two integers, a and b, then there must exist q and r such that the given condition (a = bq + r where 0 ≤ r < b) is satisfied.

Euclid’s Division Lemma (similar to a theorem) states that given two positive numbers a and b, there exist unique integers q and r such that (a = bq + r, 0 ≤ r < b). The quotient is q, and the remainder is r. The quotient and remainder are both distinct.

Summary:

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

2 is the value of ‘m’ for HCF of 408 and 1032 which is expressible in the form of 1032 m − 408 × 5. To find the value of ‘m’ use Euclid’s division algorithm. According to the Euclid’s Division Algorithm, if there are any two integers, a and b, then there must be q and r.

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