Highest Common Factor of 930, 680, 213 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 930, 680, 213 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 930, 680, 213 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 930, 680, 213 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 930, 680, 213 is 1.

HCF(930, 680, 213) = 1

HCF of 930, 680, 213 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 930, 680, 213 is 1.

Highest Common Factor of 930,680,213 using Euclid's algorithm

Highest Common Factor of 930,680,213 is 1

Step 1: Since 930 > 680, we apply the division lemma to 930 and 680, to get

930 = 680 x 1 + 250

Step 2: Since the reminder 680 ≠ 0, we apply division lemma to 250 and 680, to get

680 = 250 x 2 + 180

Step 3: We consider the new divisor 250 and the new remainder 180, and apply the division lemma to get

250 = 180 x 1 + 70

We consider the new divisor 180 and the new remainder 70,and apply the division lemma to get

180 = 70 x 2 + 40

We consider the new divisor 70 and the new remainder 40,and apply the division lemma to get

70 = 40 x 1 + 30

We consider the new divisor 40 and the new remainder 30,and apply the division lemma to get

40 = 30 x 1 + 10

We consider the new divisor 30 and the new remainder 10,and apply the division lemma to get

30 = 10 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 930 and 680 is 10

Notice that 10 = HCF(30,10) = HCF(40,30) = HCF(70,40) = HCF(180,70) = HCF(250,180) = HCF(680,250) = HCF(930,680) .

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

Step 1: Since 213 > 10, we apply the division lemma to 213 and 10, to get

213 = 10 x 21 + 3

Step 2: Since the reminder 10 ≠ 0, we apply division lemma to 3 and 10, to get

10 = 3 x 3 + 1

Step 3: We consider the new divisor 3 and the new remainder 1, and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 10 and 213 is 1

Notice that 1 = HCF(3,1) = HCF(10,3) = HCF(213,10) .

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Frequently Asked Questions on HCF of 930, 680, 213 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 930, 680, 213?

Answer: HCF of 930, 680, 213 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 930, 680, 213 using Euclid's Algorithm?

Answer: For arbitrary numbers 930, 680, 213 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.