Highest Common Factor of 630, 174, 214, 807 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 630, 174, 214, 807 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 630, 174, 214, 807 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 630, 174, 214, 807 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 630, 174, 214, 807 is 1.

HCF(630, 174, 214, 807) = 1

HCF of 630, 174, 214, 807 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 630, 174, 214, 807 is 1.

Highest Common Factor of 630,174,214,807 using Euclid's algorithm

Highest Common Factor of 630,174,214,807 is 1

Step 1: Since 630 > 174, we apply the division lemma to 630 and 174, to get

630 = 174 x 3 + 108

Step 2: Since the reminder 174 ≠ 0, we apply division lemma to 108 and 174, to get

174 = 108 x 1 + 66

Step 3: We consider the new divisor 108 and the new remainder 66, and apply the division lemma to get

108 = 66 x 1 + 42

We consider the new divisor 66 and the new remainder 42,and apply the division lemma to get

66 = 42 x 1 + 24

We consider the new divisor 42 and the new remainder 24,and apply the division lemma to get

42 = 24 x 1 + 18

We consider the new divisor 24 and the new remainder 18,and apply the division lemma to get

24 = 18 x 1 + 6

We consider the new divisor 18 and the new remainder 6,and apply the division lemma to get

18 = 6 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 630 and 174 is 6

Notice that 6 = HCF(18,6) = HCF(24,18) = HCF(42,24) = HCF(66,42) = HCF(108,66) = HCF(174,108) = HCF(630,174) .

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

Step 1: Since 214 > 6, we apply the division lemma to 214 and 6, to get

214 = 6 x 35 + 4

Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 4 and 6, to get

6 = 4 x 1 + 2

Step 3: 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 6 and 214 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(214,6) .

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

Step 1: Since 807 > 2, we apply the division lemma to 807 and 2, to get

807 = 2 x 403 + 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 807 is 1

Notice that 1 = HCF(2,1) = HCF(807,2) .

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Frequently Asked Questions on HCF of 630, 174, 214, 807 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 630, 174, 214, 807?

Answer: HCF of 630, 174, 214, 807 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 630, 174, 214, 807 using Euclid's Algorithm?

Answer: For arbitrary numbers 630, 174, 214, 807 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.