Highest Common Factor of 968, 366, 380 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 968, 366, 380 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 968, 366, 380 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 968, 366, 380 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 968, 366, 380 is 2.

HCF(968, 366, 380) = 2

HCF of 968, 366, 380 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 968, 366, 380 is 2.

Highest Common Factor of 968,366,380 using Euclid's algorithm

Highest Common Factor of 968,366,380 is 2

Step 1: Since 968 > 366, we apply the division lemma to 968 and 366, to get

968 = 366 x 2 + 236

Step 2: Since the reminder 366 ≠ 0, we apply division lemma to 236 and 366, to get

366 = 236 x 1 + 130

Step 3: We consider the new divisor 236 and the new remainder 130, and apply the division lemma to get

236 = 130 x 1 + 106

We consider the new divisor 130 and the new remainder 106,and apply the division lemma to get

130 = 106 x 1 + 24

We consider the new divisor 106 and the new remainder 24,and apply the division lemma to get

106 = 24 x 4 + 10

We consider the new divisor 24 and the new remainder 10,and apply the division lemma to get

24 = 10 x 2 + 4

We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get

10 = 4 x 2 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 968 and 366 is 2

Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(24,10) = HCF(106,24) = HCF(130,106) = HCF(236,130) = HCF(366,236) = HCF(968,366) .

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

Step 1: Since 380 > 2, we apply the division lemma to 380 and 2, to get

380 = 2 x 190 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 380 is 2

Notice that 2 = HCF(380,2) .

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Frequently Asked Questions on HCF of 968, 366, 380 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 968, 366, 380?

Answer: HCF of 968, 366, 380 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 968, 366, 380 using Euclid's Algorithm?

Answer: For arbitrary numbers 968, 366, 380 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.