Highest Common Factor of 67, 40 using Euclid's algorithm

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 67, 40 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 67, 40 is 1 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.

Consider we have numbers 67, 40 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b

Highest common factor (HCF) of 67, 40 is 1.

HCF(67, 40) = 1

HCF of 67, 40 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

HCF of:

Highest common factor (HCF) of 67, 40 is 1.

Highest Common Factor of 67,40 using Euclid's algorithm

Highest Common Factor of 67,40 is 1

Step 1: Since 67 > 40, we apply the division lemma to 67 and 40, to get

67 = 40 x 1 + 27

Step 2: Since the reminder 40 ≠ 0, we apply division lemma to 27 and 40, to get

40 = 27 x 1 + 13

Step 3: We consider the new divisor 27 and the new remainder 13, and apply the division lemma to get

27 = 13 x 2 + 1

We consider the new divisor 13 and the new remainder 1, and apply the division lemma to get

13 = 1 x 13 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 67 and 40 is 1

Notice that 1 = HCF(13,1) = HCF(27,13) = HCF(40,27) = HCF(67,40) .

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Frequently Asked Questions on HCF of 67, 40 using Euclid's Algorithm

1. What is the Euclid division algorithm?

Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.

2. what is the HCF of 67, 40?

Answer: HCF of 67, 40 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 67, 40 using Euclid's Algorithm?

Answer: For arbitrary numbers 67, 40 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.