Highest Common Factor of 712, 920, 347, 74 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 712, 920, 347, 74 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 712, 920, 347, 74 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 712, 920, 347, 74 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 712, 920, 347, 74 is 1.

HCF(712, 920, 347, 74) = 1

HCF of 712, 920, 347, 74 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 712, 920, 347, 74 is 1.

Highest Common Factor of 712,920,347,74 using Euclid's algorithm

Highest Common Factor of 712,920,347,74 is 1

Step 1: Since 920 > 712, we apply the division lemma to 920 and 712, to get

920 = 712 x 1 + 208

Step 2: Since the reminder 712 ≠ 0, we apply division lemma to 208 and 712, to get

712 = 208 x 3 + 88

Step 3: We consider the new divisor 208 and the new remainder 88, and apply the division lemma to get

208 = 88 x 2 + 32

We consider the new divisor 88 and the new remainder 32,and apply the division lemma to get

88 = 32 x 2 + 24

We consider the new divisor 32 and the new remainder 24,and apply the division lemma to get

32 = 24 x 1 + 8

We consider the new divisor 24 and the new remainder 8,and apply the division lemma to get

24 = 8 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 712 and 920 is 8

Notice that 8 = HCF(24,8) = HCF(32,24) = HCF(88,32) = HCF(208,88) = HCF(712,208) = HCF(920,712) .

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

Step 1: Since 347 > 8, we apply the division lemma to 347 and 8, to get

347 = 8 x 43 + 3

Step 2: Since the reminder 8 ≠ 0, we apply division lemma to 3 and 8, to get

8 = 3 x 2 + 2

Step 3: We consider the new divisor 3 and the new remainder 2, and apply the division lemma to get

3 = 2 x 1 + 1

We consider the new divisor 2 and the new remainder 1, and apply the division lemma 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 8 and 347 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(347,8) .

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

Step 1: Since 74 > 1, we apply the division lemma to 74 and 1, to get

74 = 1 x 74 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 74 is 1

Notice that 1 = HCF(74,1) .

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Frequently Asked Questions on HCF of 712, 920, 347, 74 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 712, 920, 347, 74?

Answer: HCF of 712, 920, 347, 74 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 712, 920, 347, 74 using Euclid's Algorithm?

Answer: For arbitrary numbers 712, 920, 347, 74 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.