Highest Common Factor of 7174, 5709 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 7174, 5709 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 7174, 5709 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 7174, 5709 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 7174, 5709 is 1.

HCF(7174, 5709) = 1

HCF of 7174, 5709 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 7174, 5709 is 1.

Highest Common Factor of 7174,5709 using Euclid's algorithm

Highest Common Factor of 7174,5709 is 1

Step 1: Since 7174 > 5709, we apply the division lemma to 7174 and 5709, to get

7174 = 5709 x 1 + 1465

Step 2: Since the reminder 5709 ≠ 0, we apply division lemma to 1465 and 5709, to get

5709 = 1465 x 3 + 1314

Step 3: We consider the new divisor 1465 and the new remainder 1314, and apply the division lemma to get

1465 = 1314 x 1 + 151

We consider the new divisor 1314 and the new remainder 151,and apply the division lemma to get

1314 = 151 x 8 + 106

We consider the new divisor 151 and the new remainder 106,and apply the division lemma to get

151 = 106 x 1 + 45

We consider the new divisor 106 and the new remainder 45,and apply the division lemma to get

106 = 45 x 2 + 16

We consider the new divisor 45 and the new remainder 16,and apply the division lemma to get

45 = 16 x 2 + 13

We consider the new divisor 16 and the new remainder 13,and apply the division lemma to get

16 = 13 x 1 + 3

We consider the new divisor 13 and the new remainder 3,and apply the division lemma to get

13 = 3 x 4 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 7174 and 5709 is 1

Notice that 1 = HCF(3,1) = HCF(13,3) = HCF(16,13) = HCF(45,16) = HCF(106,45) = HCF(151,106) = HCF(1314,151) = HCF(1465,1314) = HCF(5709,1465) = HCF(7174,5709) .

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Frequently Asked Questions on HCF of 7174, 5709 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 7174, 5709?

Answer: HCF of 7174, 5709 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 7174, 5709 using Euclid's Algorithm?

Answer: For arbitrary numbers 7174, 5709 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.