Highest Common Factor of 66, 14 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 66, 14 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 66, 14 is 2 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 66, 14 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 66, 14 is 2.

HCF(66, 14) = 2

HCF of 66, 14 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 66, 14 is 2.

Highest Common Factor of 66,14 using Euclid's algorithm

Highest Common Factor of 66,14 is 2

Step 1: Since 66 > 14, we apply the division lemma to 66 and 14, to get

66 = 14 x 4 + 10

Step 2: Since the reminder 14 ≠ 0, we apply division lemma to 10 and 14, to get

14 = 10 x 1 + 4

Step 3: We consider the new divisor 10 and the new remainder 4, and apply the division lemma to get

10 = 4 x 2 + 2

We consider the new divisor 4 and the new remainder 2, and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 66 and 14 is 2

Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(14,10) = HCF(66,14) .

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Frequently Asked Questions on HCF of 66, 14 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 66, 14?

Answer: HCF of 66, 14 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 66, 14 using Euclid's Algorithm?

Answer: For arbitrary numbers 66, 14 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.