If the HCF of 65 and 117 is expressible in form 65m - 117, then the value of m is 4. (a) True (b) False

By Ritesh|Updated : November 13th, 2022

The value of m is 4 is false. We know that by using Euclid's division algorithm

b = aq + r, 0 ≤ r < a [dividend = divisor x quotient + remainder]

Now by applying Euclid's division algorithm to the given numbers:

117 = 65 x 1 + 52…. (i)

65 = 52 x 1 + 13…. (ii)

52 = 13 x 4 + 0

Therefore,

HCF (65, 117) = 13

And, also we have, HCF (65 117) = 65 m - 117

From Eqs. (i) and (ii)

65m - 117 = 13

On rearranging we get:

65m = 130

m = 2

therefore the value of m is 2.

How to find Highest Common Factor?

The abbreviation for this phrase is Highest Common Factor. The HCF of two numbers is the highest factor that may divide two integers equally. It is possible to evaluate HCF using two or more numbers. It is the most effective divisor for any pair of numbers that may evenly or totally divide the entered values.

There are two ways we can determine the HCF of any given set of numbers:

  1. by prime factorization method
  2. by division method

Shortcut method

Step 1: procedures for calculating the HCF of any given set of numbers.

Divide the larger number by the smaller number, like in Larger Number/Smaller Number, in step one.

Step 2: Deduct the residual from the divisor in step 1.

The remainder divisor in Step 1

Step 3: Deduct the residue one more time from the divisor in step 2.

The remainder divisor in Step 2

Step 4: Continue until there is no longer any money available.

Step 5: The previous step's divisor is the HCF.

Summary:

If the HCF of 65 and 117 is expressible in form 65m - 117, then the value of m is 4. (a) True (b) False

The statement “If the HCF of 65 and 117 is expressible in form 65m - 117, then the value of m is 4.” is false. HCF or Highest Common Factor is the greatest number that divides each of two or more numbers. HCF is also called the Greatest Common Measure (GCM) and Greatest Common Divisor(GCD).

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