Highest Common Factor of 420, 668, 70 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 420, 668, 70 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 420, 668, 70 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 420, 668, 70 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 420, 668, 70 is 2.

HCF(420, 668, 70) = 2

HCF of 420, 668, 70 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 420, 668, 70 is 2.

Highest Common Factor of 420,668,70 using Euclid's algorithm

Highest Common Factor of 420,668,70 is 2

Step 1: Since 668 > 420, we apply the division lemma to 668 and 420, to get

668 = 420 x 1 + 248

Step 2: Since the reminder 420 ≠ 0, we apply division lemma to 248 and 420, to get

420 = 248 x 1 + 172

Step 3: We consider the new divisor 248 and the new remainder 172, and apply the division lemma to get

248 = 172 x 1 + 76

We consider the new divisor 172 and the new remainder 76,and apply the division lemma to get

172 = 76 x 2 + 20

We consider the new divisor 76 and the new remainder 20,and apply the division lemma to get

76 = 20 x 3 + 16

We consider the new divisor 20 and the new remainder 16,and apply the division lemma to get

20 = 16 x 1 + 4

We consider the new divisor 16 and the new remainder 4,and apply the division lemma to get

16 = 4 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 420 and 668 is 4

Notice that 4 = HCF(16,4) = HCF(20,16) = HCF(76,20) = HCF(172,76) = HCF(248,172) = HCF(420,248) = HCF(668,420) .

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

Step 1: Since 70 > 4, we apply the division lemma to 70 and 4, to get

70 = 4 x 17 + 2

Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, 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 4 and 70 is 2

Notice that 2 = HCF(4,2) = HCF(70,4) .

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Frequently Asked Questions on HCF of 420, 668, 70 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 420, 668, 70?

Answer: HCF of 420, 668, 70 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 420, 668, 70 using Euclid's Algorithm?

Answer: For arbitrary numbers 420, 668, 70 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.