Highest Common Factor of 454, 278, 775 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 454, 278, 775 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 454, 278, 775 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 454, 278, 775 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 454, 278, 775 is 1.

HCF(454, 278, 775) = 1

HCF of 454, 278, 775 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 454, 278, 775 is 1.

Highest Common Factor of 454,278,775 using Euclid's algorithm

Highest Common Factor of 454,278,775 is 1

Step 1: Since 454 > 278, we apply the division lemma to 454 and 278, to get

454 = 278 x 1 + 176

Step 2: Since the reminder 278 ≠ 0, we apply division lemma to 176 and 278, to get

278 = 176 x 1 + 102

Step 3: We consider the new divisor 176 and the new remainder 102, and apply the division lemma to get

176 = 102 x 1 + 74

We consider the new divisor 102 and the new remainder 74,and apply the division lemma to get

102 = 74 x 1 + 28

We consider the new divisor 74 and the new remainder 28,and apply the division lemma to get

74 = 28 x 2 + 18

We consider the new divisor 28 and the new remainder 18,and apply the division lemma to get

28 = 18 x 1 + 10

We consider the new divisor 18 and the new remainder 10,and apply the division lemma to get

18 = 10 x 1 + 8

We consider the new divisor 10 and the new remainder 8,and apply the division lemma to get

10 = 8 x 1 + 2

We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get

8 = 2 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 454 and 278 is 2

Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(18,10) = HCF(28,18) = HCF(74,28) = HCF(102,74) = HCF(176,102) = HCF(278,176) = HCF(454,278) .

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

Step 1: Since 775 > 2, we apply the division lemma to 775 and 2, to get

775 = 2 x 387 + 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 775 is 1

Notice that 1 = HCF(2,1) = HCF(775,2) .

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Frequently Asked Questions on HCF of 454, 278, 775 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 454, 278, 775?

Answer: HCF of 454, 278, 775 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 454, 278, 775 using Euclid's Algorithm?

Answer: For arbitrary numbers 454, 278, 775 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.