Highest Common Factor of 380, 608, 368 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 380, 608, 368 i.e. 4 the largest integer that leaves a remainder zero for all numbers.

HCF of 380, 608, 368 is 4 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 380, 608, 368 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 380, 608, 368 is 4.

HCF(380, 608, 368) = 4

HCF of 380, 608, 368 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 380, 608, 368 is 4.

Highest Common Factor of 380,608,368 using Euclid's algorithm

Highest Common Factor of 380,608,368 is 4

Step 1: Since 608 > 380, we apply the division lemma to 608 and 380, to get

608 = 380 x 1 + 228

Step 2: Since the reminder 380 ≠ 0, we apply division lemma to 228 and 380, to get

380 = 228 x 1 + 152

Step 3: We consider the new divisor 228 and the new remainder 152, and apply the division lemma to get

228 = 152 x 1 + 76

We consider the new divisor 152 and the new remainder 76, and apply the division lemma to get

152 = 76 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 76, the HCF of 380 and 608 is 76

Notice that 76 = HCF(152,76) = HCF(228,152) = HCF(380,228) = HCF(608,380) .

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

Step 1: Since 368 > 76, we apply the division lemma to 368 and 76, to get

368 = 76 x 4 + 64

Step 2: Since the reminder 76 ≠ 0, we apply division lemma to 64 and 76, to get

76 = 64 x 1 + 12

Step 3: We consider the new divisor 64 and the new remainder 12, and apply the division lemma to get

64 = 12 x 5 + 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 76 and 368 is 4

Notice that 4 = HCF(12,4) = HCF(64,12) = HCF(76,64) = HCF(368,76) .

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Frequently Asked Questions on HCF of 380, 608, 368 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 380, 608, 368?

Answer: HCF of 380, 608, 368 is 4 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 380, 608, 368 using Euclid's Algorithm?

Answer: For arbitrary numbers 380, 608, 368 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.