Highest Common Factor of 620, 174, 29, 374 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 620, 174, 29, 374 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 620, 174, 29, 374 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 620, 174, 29, 374 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 620, 174, 29, 374 is 1.

HCF(620, 174, 29, 374) = 1

HCF of 620, 174, 29, 374 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 620, 174, 29, 374 is 1.

Highest Common Factor of 620,174,29,374 using Euclid's algorithm

Highest Common Factor of 620,174,29,374 is 1

Step 1: Since 620 > 174, we apply the division lemma to 620 and 174, to get

620 = 174 x 3 + 98

Step 2: Since the reminder 174 ≠ 0, we apply division lemma to 98 and 174, to get

174 = 98 x 1 + 76

Step 3: We consider the new divisor 98 and the new remainder 76, and apply the division lemma to get

98 = 76 x 1 + 22

We consider the new divisor 76 and the new remainder 22,and apply the division lemma to get

76 = 22 x 3 + 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 620 and 174 is 2

Notice that 2 = HCF(10,2) = HCF(22,10) = HCF(76,22) = HCF(98,76) = HCF(174,98) = HCF(620,174) .

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

Step 1: Since 29 > 2, we apply the division lemma to 29 and 2, to get

29 = 2 x 14 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 29 is 1

Notice that 1 = HCF(2,1) = HCF(29,2) .

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

Step 1: Since 374 > 1, we apply the division lemma to 374 and 1, to get

374 = 1 x 374 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 374 is 1

Notice that 1 = HCF(374,1) .

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Frequently Asked Questions on HCF of 620, 174, 29, 374 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 620, 174, 29, 374?

Answer: HCF of 620, 174, 29, 374 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 620, 174, 29, 374 using Euclid's Algorithm?

Answer: For arbitrary numbers 620, 174, 29, 374 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.