Highest Common Factor of 778, 498, 541 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 778, 498, 541 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 778, 498, 541 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 778, 498, 541 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 778, 498, 541 is 1.

HCF(778, 498, 541) = 1

HCF of 778, 498, 541 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 778, 498, 541 is 1.

Highest Common Factor of 778,498,541 using Euclid's algorithm

Highest Common Factor of 778,498,541 is 1

Step 1: Since 778 > 498, we apply the division lemma to 778 and 498, to get

778 = 498 x 1 + 280

Step 2: Since the reminder 498 ≠ 0, we apply division lemma to 280 and 498, to get

498 = 280 x 1 + 218

Step 3: We consider the new divisor 280 and the new remainder 218, and apply the division lemma to get

280 = 218 x 1 + 62

We consider the new divisor 218 and the new remainder 62,and apply the division lemma to get

218 = 62 x 3 + 32

We consider the new divisor 62 and the new remainder 32,and apply the division lemma to get

62 = 32 x 1 + 30

We consider the new divisor 32 and the new remainder 30,and apply the division lemma to get

32 = 30 x 1 + 2

We consider the new divisor 30 and the new remainder 2,and apply the division lemma to get

30 = 2 x 15 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 778 and 498 is 2

Notice that 2 = HCF(30,2) = HCF(32,30) = HCF(62,32) = HCF(218,62) = HCF(280,218) = HCF(498,280) = HCF(778,498) .

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

Step 1: Since 541 > 2, we apply the division lemma to 541 and 2, to get

541 = 2 x 270 + 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 541 is 1

Notice that 1 = HCF(2,1) = HCF(541,2) .

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Frequently Asked Questions on HCF of 778, 498, 541 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 778, 498, 541?

Answer: HCF of 778, 498, 541 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 778, 498, 541 using Euclid's Algorithm?

Answer: For arbitrary numbers 778, 498, 541 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.