Highest Common Factor of 374, 912, 709 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 374, 912, 709 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 374, 912, 709 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 374, 912, 709 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 374, 912, 709 is 1.

HCF(374, 912, 709) = 1

HCF of 374, 912, 709 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 374, 912, 709 is 1.

Highest Common Factor of 374,912,709 using Euclid's algorithm

Highest Common Factor of 374,912,709 is 1

Step 1: Since 912 > 374, we apply the division lemma to 912 and 374, to get

912 = 374 x 2 + 164

Step 2: Since the reminder 374 ≠ 0, we apply division lemma to 164 and 374, to get

374 = 164 x 2 + 46

Step 3: We consider the new divisor 164 and the new remainder 46, and apply the division lemma to get

164 = 46 x 3 + 26

We consider the new divisor 46 and the new remainder 26,and apply the division lemma to get

46 = 26 x 1 + 20

We consider the new divisor 26 and the new remainder 20,and apply the division lemma to get

26 = 20 x 1 + 6

We consider the new divisor 20 and the new remainder 6,and apply the division lemma to get

20 = 6 x 3 + 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 374 and 912 is 2

Notice that 2 = HCF(6,2) = HCF(20,6) = HCF(26,20) = HCF(46,26) = HCF(164,46) = HCF(374,164) = HCF(912,374) .

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

Step 1: Since 709 > 2, we apply the division lemma to 709 and 2, to get

709 = 2 x 354 + 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 709 is 1

Notice that 1 = HCF(2,1) = HCF(709,2) .

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Frequently Asked Questions on HCF of 374, 912, 709 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 374, 912, 709?

Answer: HCF of 374, 912, 709 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 374, 912, 709 using Euclid's Algorithm?

Answer: For arbitrary numbers 374, 912, 709 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.