Highest Common Factor of 684, 412, 44 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 684, 412, 44 i.e. 4 the largest integer that leaves a remainder zero for all numbers.

HCF of 684, 412, 44 is 4 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 684, 412, 44 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 684, 412, 44 is 4.

HCF(684, 412, 44) = 4

HCF of 684, 412, 44 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 684, 412, 44 is 4.

Highest Common Factor of 684,412,44 using Euclid's algorithm

Highest Common Factor of 684,412,44 is 4

Step 1: Since 684 > 412, we apply the division lemma to 684 and 412, to get

684 = 412 x 1 + 272

Step 2: Since the reminder 412 ≠ 0, we apply division lemma to 272 and 412, to get

412 = 272 x 1 + 140

Step 3: We consider the new divisor 272 and the new remainder 140, and apply the division lemma to get

272 = 140 x 1 + 132

We consider the new divisor 140 and the new remainder 132,and apply the division lemma to get

140 = 132 x 1 + 8

We consider the new divisor 132 and the new remainder 8,and apply the division lemma to get

132 = 8 x 16 + 4

We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get

8 = 4 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 684 and 412 is 4

Notice that 4 = HCF(8,4) = HCF(132,8) = HCF(140,132) = HCF(272,140) = HCF(412,272) = HCF(684,412) .

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

Step 1: Since 44 > 4, we apply the division lemma to 44 and 4, to get

44 = 4 x 11 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 4 and 44 is 4

Notice that 4 = HCF(44,4) .

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Frequently Asked Questions on HCF of 684, 412, 44 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 684, 412, 44?

Answer: HCF of 684, 412, 44 is 4 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 684, 412, 44 using Euclid's Algorithm?

Answer: For arbitrary numbers 684, 412, 44 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.