Highest Common Factor of 7408, 6710, 67714 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 7408, 6710, 67714 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 7408, 6710, 67714 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 7408, 6710, 67714 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 7408, 6710, 67714 is 2.

HCF(7408, 6710, 67714) = 2

HCF of 7408, 6710, 67714 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 7408, 6710, 67714 is 2.

Highest Common Factor of 7408,6710,67714 using Euclid's algorithm

Highest Common Factor of 7408,6710,67714 is 2

Step 1: Since 7408 > 6710, we apply the division lemma to 7408 and 6710, to get

7408 = 6710 x 1 + 698

Step 2: Since the reminder 6710 ≠ 0, we apply division lemma to 698 and 6710, to get

6710 = 698 x 9 + 428

Step 3: We consider the new divisor 698 and the new remainder 428, and apply the division lemma to get

698 = 428 x 1 + 270

We consider the new divisor 428 and the new remainder 270,and apply the division lemma to get

428 = 270 x 1 + 158

We consider the new divisor 270 and the new remainder 158,and apply the division lemma to get

270 = 158 x 1 + 112

We consider the new divisor 158 and the new remainder 112,and apply the division lemma to get

158 = 112 x 1 + 46

We consider the new divisor 112 and the new remainder 46,and apply the division lemma to get

112 = 46 x 2 + 20

We consider the new divisor 46 and the new remainder 20,and apply the division lemma to get

46 = 20 x 2 + 6

We consider the new divisor 20 and the new remainder 6,and apply the division lemma to get

20 = 6 x 3 + 2

We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get

6 = 2 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 7408 and 6710 is 2

Notice that 2 = HCF(6,2) = HCF(20,6) = HCF(46,20) = HCF(112,46) = HCF(158,112) = HCF(270,158) = HCF(428,270) = HCF(698,428) = HCF(6710,698) = HCF(7408,6710) .

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

Step 1: Since 67714 > 2, we apply the division lemma to 67714 and 2, to get

67714 = 2 x 33857 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 67714 is 2

Notice that 2 = HCF(67714,2) .

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Frequently Asked Questions on HCF of 7408, 6710, 67714 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 7408, 6710, 67714?

Answer: HCF of 7408, 6710, 67714 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 7408, 6710, 67714 using Euclid's Algorithm?

Answer: For arbitrary numbers 7408, 6710, 67714 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.