Highest Common Factor of 74, 43, 68, 714 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 74, 43, 68, 714 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 74, 43, 68, 714 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 74, 43, 68, 714 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 74, 43, 68, 714 is 1.

HCF(74, 43, 68, 714) = 1

HCF of 74, 43, 68, 714 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 74, 43, 68, 714 is 1.

Highest Common Factor of 74,43,68,714 using Euclid's algorithm

Highest Common Factor of 74,43,68,714 is 1

Step 1: Since 74 > 43, we apply the division lemma to 74 and 43, to get

74 = 43 x 1 + 31

Step 2: Since the reminder 43 ≠ 0, we apply division lemma to 31 and 43, to get

43 = 31 x 1 + 12

Step 3: We consider the new divisor 31 and the new remainder 12, and apply the division lemma to get

31 = 12 x 2 + 7

We consider the new divisor 12 and the new remainder 7,and apply the division lemma to get

12 = 7 x 1 + 5

We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get

7 = 5 x 1 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 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 74 and 43 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(12,7) = HCF(31,12) = HCF(43,31) = HCF(74,43) .

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

Step 1: Since 68 > 1, we apply the division lemma to 68 and 1, to get

68 = 1 x 68 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 68 is 1

Notice that 1 = HCF(68,1) .

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

Step 1: Since 714 > 1, we apply the division lemma to 714 and 1, to get

714 = 1 x 714 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 714 is 1

Notice that 1 = HCF(714,1) .

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Frequently Asked Questions on HCF of 74, 43, 68, 714 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 74, 43, 68, 714?

Answer: HCF of 74, 43, 68, 714 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 74, 43, 68, 714 using Euclid's Algorithm?

Answer: For arbitrary numbers 74, 43, 68, 714 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.