Highest Common Factor of 7178, 3328, 91700 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 7178, 3328, 91700 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 7178, 3328, 91700 is 2 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 7178, 3328, 91700 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 7178, 3328, 91700 is 2.

HCF(7178, 3328, 91700) = 2

HCF of 7178, 3328, 91700 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 7178, 3328, 91700 is 2.

Highest Common Factor of 7178,3328,91700 using Euclid's algorithm

Highest Common Factor of 7178,3328,91700 is 2

Step 1: Since 7178 > 3328, we apply the division lemma to 7178 and 3328, to get

7178 = 3328 x 2 + 522

Step 2: Since the reminder 3328 ≠ 0, we apply division lemma to 522 and 3328, to get

3328 = 522 x 6 + 196

Step 3: We consider the new divisor 522 and the new remainder 196, and apply the division lemma to get

522 = 196 x 2 + 130

We consider the new divisor 196 and the new remainder 130,and apply the division lemma to get

196 = 130 x 1 + 66

We consider the new divisor 130 and the new remainder 66,and apply the division lemma to get

130 = 66 x 1 + 64

We consider the new divisor 66 and the new remainder 64,and apply the division lemma to get

66 = 64 x 1 + 2

We consider the new divisor 64 and the new remainder 2,and apply the division lemma to get

64 = 2 x 32 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 7178 and 3328 is 2

Notice that 2 = HCF(64,2) = HCF(66,64) = HCF(130,66) = HCF(196,130) = HCF(522,196) = HCF(3328,522) = HCF(7178,3328) .

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

Step 1: Since 91700 > 2, we apply the division lemma to 91700 and 2, to get

91700 = 2 x 45850 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 91700 is 2

Notice that 2 = HCF(91700,2) .

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Frequently Asked Questions on HCF of 7178, 3328, 91700 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 7178, 3328, 91700?

Answer: HCF of 7178, 3328, 91700 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 7178, 3328, 91700 using Euclid's Algorithm?

Answer: For arbitrary numbers 7178, 3328, 91700 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.