Highest Common Factor of 164, 613, 624 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, 613, 624 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 164, 613, 624 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 164, 613, 624 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, 613, 624 is 1.

HCF(164, 613, 624) = 1

HCF of 164, 613, 624 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, 613, 624 is 1.

Highest Common Factor of 164,613,624 using Euclid's algorithm

Highest Common Factor of 164,613,624 is 1

Step 1: Since 613 > 164, we apply the division lemma to 613 and 164, to get

613 = 164 x 3 + 121

Step 2: Since the reminder 164 ≠ 0, we apply division lemma to 121 and 164, to get

164 = 121 x 1 + 43

Step 3: We consider the new divisor 121 and the new remainder 43, and apply the division lemma to get

121 = 43 x 2 + 35

We consider the new divisor 43 and the new remainder 35,and apply the division lemma to get

43 = 35 x 1 + 8

We consider the new divisor 35 and the new remainder 8,and apply the division lemma to get

35 = 8 x 4 + 3

We consider the new divisor 8 and the new remainder 3,and apply the division lemma to get

8 = 3 x 2 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 164 and 613 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(35,8) = HCF(43,35) = HCF(121,43) = HCF(164,121) = HCF(613,164) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 624 > 1, we apply the division lemma to 624 and 1, to get

624 = 1 x 624 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 624 is 1

Notice that 1 = HCF(624,1) .

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Frequently Asked Questions on HCF of 164, 613, 624 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, 613, 624?

Answer: HCF of 164, 613, 624 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 164, 613, 624 using Euclid's Algorithm?

Answer: For arbitrary numbers 164, 613, 624 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.