Highest Common Factor of 6452, 3490, 66872 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 6452, 3490, 66872 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 6452, 3490, 66872 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 6452, 3490, 66872 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 6452, 3490, 66872 is 2.

HCF(6452, 3490, 66872) = 2

HCF of 6452, 3490, 66872 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 6452, 3490, 66872 is 2.

Highest Common Factor of 6452,3490,66872 using Euclid's algorithm

Highest Common Factor of 6452,3490,66872 is 2

Step 1: Since 6452 > 3490, we apply the division lemma to 6452 and 3490, to get

6452 = 3490 x 1 + 2962

Step 2: Since the reminder 3490 ≠ 0, we apply division lemma to 2962 and 3490, to get

3490 = 2962 x 1 + 528

Step 3: We consider the new divisor 2962 and the new remainder 528, and apply the division lemma to get

2962 = 528 x 5 + 322

We consider the new divisor 528 and the new remainder 322,and apply the division lemma to get

528 = 322 x 1 + 206

We consider the new divisor 322 and the new remainder 206,and apply the division lemma to get

322 = 206 x 1 + 116

We consider the new divisor 206 and the new remainder 116,and apply the division lemma to get

206 = 116 x 1 + 90

We consider the new divisor 116 and the new remainder 90,and apply the division lemma to get

116 = 90 x 1 + 26

We consider the new divisor 90 and the new remainder 26,and apply the division lemma to get

90 = 26 x 3 + 12

We consider the new divisor 26 and the new remainder 12,and apply the division lemma to get

26 = 12 x 2 + 2

We consider the new divisor 12 and the new remainder 2,and apply the division lemma to get

12 = 2 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 6452 and 3490 is 2

Notice that 2 = HCF(12,2) = HCF(26,12) = HCF(90,26) = HCF(116,90) = HCF(206,116) = HCF(322,206) = HCF(528,322) = HCF(2962,528) = HCF(3490,2962) = HCF(6452,3490) .

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

Step 1: Since 66872 > 2, we apply the division lemma to 66872 and 2, to get

66872 = 2 x 33436 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 66872 is 2

Notice that 2 = HCF(66872,2) .

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Frequently Asked Questions on HCF of 6452, 3490, 66872 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 6452, 3490, 66872?

Answer: HCF of 6452, 3490, 66872 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 6452, 3490, 66872 using Euclid's Algorithm?

Answer: For arbitrary numbers 6452, 3490, 66872 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.