Highest Common Factor of 392, 726, 123 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 392, 726, 123 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 392, 726, 123 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 392, 726, 123 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 392, 726, 123 is 1.

HCF(392, 726, 123) = 1

HCF of 392, 726, 123 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 392, 726, 123 is 1.

Highest Common Factor of 392,726,123 using Euclid's algorithm

Highest Common Factor of 392,726,123 is 1

Step 1: Since 726 > 392, we apply the division lemma to 726 and 392, to get

726 = 392 x 1 + 334

Step 2: Since the reminder 392 ≠ 0, we apply division lemma to 334 and 392, to get

392 = 334 x 1 + 58

Step 3: We consider the new divisor 334 and the new remainder 58, and apply the division lemma to get

334 = 58 x 5 + 44

We consider the new divisor 58 and the new remainder 44,and apply the division lemma to get

58 = 44 x 1 + 14

We consider the new divisor 44 and the new remainder 14,and apply the division lemma to get

44 = 14 x 3 + 2

We consider the new divisor 14 and the new remainder 2,and apply the division lemma to get

14 = 2 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 392 and 726 is 2

Notice that 2 = HCF(14,2) = HCF(44,14) = HCF(58,44) = HCF(334,58) = HCF(392,334) = HCF(726,392) .

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

Step 1: Since 123 > 2, we apply the division lemma to 123 and 2, to get

123 = 2 x 61 + 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 123 is 1

Notice that 1 = HCF(2,1) = HCF(123,2) .

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Frequently Asked Questions on HCF of 392, 726, 123 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 392, 726, 123?

Answer: HCF of 392, 726, 123 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 392, 726, 123 using Euclid's Algorithm?

Answer: For arbitrary numbers 392, 726, 123 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.