Highest Common Factor of 348, 656, 117, 41 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 348, 656, 117, 41 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 348, 656, 117, 41 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 348, 656, 117, 41 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 348, 656, 117, 41 is 1.

HCF(348, 656, 117, 41) = 1

HCF of 348, 656, 117, 41 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 348, 656, 117, 41 is 1.

Highest Common Factor of 348,656,117,41 using Euclid's algorithm

Highest Common Factor of 348,656,117,41 is 1

Step 1: Since 656 > 348, we apply the division lemma to 656 and 348, to get

656 = 348 x 1 + 308

Step 2: Since the reminder 348 ≠ 0, we apply division lemma to 308 and 348, to get

348 = 308 x 1 + 40

Step 3: We consider the new divisor 308 and the new remainder 40, and apply the division lemma to get

308 = 40 x 7 + 28

We consider the new divisor 40 and the new remainder 28,and apply the division lemma to get

40 = 28 x 1 + 12

We consider the new divisor 28 and the new remainder 12,and apply the division lemma to get

28 = 12 x 2 + 4

We consider the new divisor 12 and the new remainder 4,and apply the division lemma to get

12 = 4 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 348 and 656 is 4

Notice that 4 = HCF(12,4) = HCF(28,12) = HCF(40,28) = HCF(308,40) = HCF(348,308) = HCF(656,348) .

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

Step 1: Since 117 > 4, we apply the division lemma to 117 and 4, to get

117 = 4 x 29 + 1

Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 1 and 4, to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 4 and 117 is 1

Notice that 1 = HCF(4,1) = HCF(117,4) .

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

Step 1: Since 41 > 1, we apply the division lemma to 41 and 1, to get

41 = 1 x 41 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 41 is 1

Notice that 1 = HCF(41,1) .

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Frequently Asked Questions on HCF of 348, 656, 117, 41 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 348, 656, 117, 41?

Answer: HCF of 348, 656, 117, 41 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 348, 656, 117, 41 using Euclid's Algorithm?

Answer: For arbitrary numbers 348, 656, 117, 41 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.