Highest Common Factor of 66, 154 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, 154 i.e. 22 the largest integer that leaves a remainder zero for all numbers.

HCF of 66, 154 is 22 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, 154 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, 154 is 22.

HCF(66, 154) = 22

HCF of 66, 154 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, 154 is 22.

Highest Common Factor of 66,154 using Euclid's algorithm

Highest Common Factor of 66,154 is 22

Step 1: Since 154 > 66, we apply the division lemma to 154 and 66, to get

154 = 66 x 2 + 22

Step 2: Since the reminder 66 ≠ 0, we apply division lemma to 22 and 66, to get

66 = 22 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 22, the HCF of 66 and 154 is 22

Notice that 22 = HCF(66,22) = HCF(154,66) .

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Frequently Asked Questions on HCF of 66, 154 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, 154?

Answer: HCF of 66, 154 is 22 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 66, 154 using Euclid's Algorithm?

Answer: For arbitrary numbers 66, 154 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.