Highest Common Factor of 378, 280, 960, 163 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 378, 280, 960, 163 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 378, 280, 960, 163 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 378, 280, 960, 163 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 378, 280, 960, 163 is 1.

HCF(378, 280, 960, 163) = 1

HCF of 378, 280, 960, 163 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 378, 280, 960, 163 is 1.

Highest Common Factor of 378,280,960,163 using Euclid's algorithm

Highest Common Factor of 378,280,960,163 is 1

Step 1: Since 378 > 280, we apply the division lemma to 378 and 280, to get

378 = 280 x 1 + 98

Step 2: Since the reminder 280 ≠ 0, we apply division lemma to 98 and 280, to get

280 = 98 x 2 + 84

Step 3: We consider the new divisor 98 and the new remainder 84, and apply the division lemma to get

98 = 84 x 1 + 14

We consider the new divisor 84 and the new remainder 14, and apply the division lemma to get

84 = 14 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 14, the HCF of 378 and 280 is 14

Notice that 14 = HCF(84,14) = HCF(98,84) = HCF(280,98) = HCF(378,280) .

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

Step 1: Since 960 > 14, we apply the division lemma to 960 and 14, to get

960 = 14 x 68 + 8

Step 2: Since the reminder 14 ≠ 0, we apply division lemma to 8 and 14, to get

14 = 8 x 1 + 6

Step 3: We consider the new divisor 8 and the new remainder 6, and apply the division lemma to get

8 = 6 x 1 + 2

We consider the new divisor 6 and the new remainder 2, and apply the division lemma to get

6 = 2 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 14 and 960 is 2

Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(14,8) = HCF(960,14) .

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

Step 1: Since 163 > 2, we apply the division lemma to 163 and 2, to get

163 = 2 x 81 + 1

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

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 163 is 1

Notice that 1 = HCF(2,1) = HCF(163,2) .

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Frequently Asked Questions on HCF of 378, 280, 960, 163 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 378, 280, 960, 163?

Answer: HCF of 378, 280, 960, 163 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 378, 280, 960, 163 using Euclid's Algorithm?

Answer: For arbitrary numbers 378, 280, 960, 163 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.