Highest Common Factor of 6670, 7358, 43875 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 6670, 7358, 43875 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 6670, 7358, 43875 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 6670, 7358, 43875 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 6670, 7358, 43875 is 1.

HCF(6670, 7358, 43875) = 1

HCF of 6670, 7358, 43875 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 6670, 7358, 43875 is 1.

Highest Common Factor of 6670,7358,43875 using Euclid's algorithm

Highest Common Factor of 6670,7358,43875 is 1

Step 1: Since 7358 > 6670, we apply the division lemma to 7358 and 6670, to get

7358 = 6670 x 1 + 688

Step 2: Since the reminder 6670 ≠ 0, we apply division lemma to 688 and 6670, to get

6670 = 688 x 9 + 478

Step 3: We consider the new divisor 688 and the new remainder 478, and apply the division lemma to get

688 = 478 x 1 + 210

We consider the new divisor 478 and the new remainder 210,and apply the division lemma to get

478 = 210 x 2 + 58

We consider the new divisor 210 and the new remainder 58,and apply the division lemma to get

210 = 58 x 3 + 36

We consider the new divisor 58 and the new remainder 36,and apply the division lemma to get

58 = 36 x 1 + 22

We consider the new divisor 36 and the new remainder 22,and apply the division lemma to get

36 = 22 x 1 + 14

We consider the new divisor 22 and the new remainder 14,and apply the division lemma to get

22 = 14 x 1 + 8

We consider the new divisor 14 and the new remainder 8,and apply the division lemma to get

14 = 8 x 1 + 6

We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get

8 = 6 x 1 + 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 6670 and 7358 is 2

Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(14,8) = HCF(22,14) = HCF(36,22) = HCF(58,36) = HCF(210,58) = HCF(478,210) = HCF(688,478) = HCF(6670,688) = HCF(7358,6670) .

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

Step 1: Since 43875 > 2, we apply the division lemma to 43875 and 2, to get

43875 = 2 x 21937 + 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 43875 is 1

Notice that 1 = HCF(2,1) = HCF(43875,2) .

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Frequently Asked Questions on HCF of 6670, 7358, 43875 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 6670, 7358, 43875?

Answer: HCF of 6670, 7358, 43875 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 6670, 7358, 43875 using Euclid's Algorithm?

Answer: For arbitrary numbers 6670, 7358, 43875 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.