Highest Common Factor of 343, 874, 788 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 343, 874, 788 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 343, 874, 788 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 343, 874, 788 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 343, 874, 788 is 1.

HCF(343, 874, 788) = 1

HCF of 343, 874, 788 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 343, 874, 788 is 1.

Highest Common Factor of 343,874,788 using Euclid's algorithm

Highest Common Factor of 343,874,788 is 1

Step 1: Since 874 > 343, we apply the division lemma to 874 and 343, to get

874 = 343 x 2 + 188

Step 2: Since the reminder 343 ≠ 0, we apply division lemma to 188 and 343, to get

343 = 188 x 1 + 155

Step 3: We consider the new divisor 188 and the new remainder 155, and apply the division lemma to get

188 = 155 x 1 + 33

We consider the new divisor 155 and the new remainder 33,and apply the division lemma to get

155 = 33 x 4 + 23

We consider the new divisor 33 and the new remainder 23,and apply the division lemma to get

33 = 23 x 1 + 10

We consider the new divisor 23 and the new remainder 10,and apply the division lemma to get

23 = 10 x 2 + 3

We consider the new divisor 10 and the new remainder 3,and apply the division lemma to get

10 = 3 x 3 + 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 343 and 874 is 1

Notice that 1 = HCF(3,1) = HCF(10,3) = HCF(23,10) = HCF(33,23) = HCF(155,33) = HCF(188,155) = HCF(343,188) = HCF(874,343) .

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

Step 1: Since 788 > 1, we apply the division lemma to 788 and 1, to get

788 = 1 x 788 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 788 is 1

Notice that 1 = HCF(788,1) .

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Frequently Asked Questions on HCF of 343, 874, 788 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 343, 874, 788?

Answer: HCF of 343, 874, 788 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 343, 874, 788 using Euclid's Algorithm?

Answer: For arbitrary numbers 343, 874, 788 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.