Highest Common Factor of 164, 306 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 164, 306 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 164, 306 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 164, 306 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 164, 306 is 2.

HCF(164, 306) = 2

HCF of 164, 306 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 164, 306 is 2.

Highest Common Factor of 164,306 using Euclid's algorithm

Highest Common Factor of 164,306 is 2

Step 1: Since 306 > 164, we apply the division lemma to 306 and 164, to get

306 = 164 x 1 + 142

Step 2: Since the reminder 164 ≠ 0, we apply division lemma to 142 and 164, to get

164 = 142 x 1 + 22

Step 3: We consider the new divisor 142 and the new remainder 22, and apply the division lemma to get

142 = 22 x 6 + 10

We consider the new divisor 22 and the new remainder 10,and apply the division lemma to get

22 = 10 x 2 + 2

We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get

10 = 2 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 164 and 306 is 2

Notice that 2 = HCF(10,2) = HCF(22,10) = HCF(142,22) = HCF(164,142) = HCF(306,164) .

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Frequently Asked Questions on HCF of 164, 306 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 164, 306?

Answer: HCF of 164, 306 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 164, 306 using Euclid's Algorithm?

Answer: For arbitrary numbers 164, 306 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.