Highest Common Factor of 124, 353, 712 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 124, 353, 712 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 124, 353, 712 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 124, 353, 712 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 124, 353, 712 is 1.

HCF(124, 353, 712) = 1

HCF of 124, 353, 712 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 124, 353, 712 is 1.

Highest Common Factor of 124,353,712 using Euclid's algorithm

Highest Common Factor of 124,353,712 is 1

Step 1: Since 353 > 124, we apply the division lemma to 353 and 124, to get

353 = 124 x 2 + 105

Step 2: Since the reminder 124 ≠ 0, we apply division lemma to 105 and 124, to get

124 = 105 x 1 + 19

Step 3: We consider the new divisor 105 and the new remainder 19, and apply the division lemma to get

105 = 19 x 5 + 10

We consider the new divisor 19 and the new remainder 10,and apply the division lemma to get

19 = 10 x 1 + 9

We consider the new divisor 10 and the new remainder 9,and apply the division lemma to get

10 = 9 x 1 + 1

We consider the new divisor 9 and the new remainder 1,and apply the division lemma to get

9 = 1 x 9 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 124 and 353 is 1

Notice that 1 = HCF(9,1) = HCF(10,9) = HCF(19,10) = HCF(105,19) = HCF(124,105) = HCF(353,124) .

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

Step 1: Since 712 > 1, we apply the division lemma to 712 and 1, to get

712 = 1 x 712 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 712 is 1

Notice that 1 = HCF(712,1) .

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Frequently Asked Questions on HCF of 124, 353, 712 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 124, 353, 712?

Answer: HCF of 124, 353, 712 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 124, 353, 712 using Euclid's Algorithm?

Answer: For arbitrary numbers 124, 353, 712 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.