Highest Common Factor of 778, 305, 534 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, 305, 534 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 778, 305, 534 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, 305, 534 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, 305, 534 is 1.

HCF(778, 305, 534) = 1

HCF of 778, 305, 534 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, 305, 534 is 1.

Highest Common Factor of 778,305,534 using Euclid's algorithm

Highest Common Factor of 778,305,534 is 1

Step 1: Since 778 > 305, we apply the division lemma to 778 and 305, to get

778 = 305 x 2 + 168

Step 2: Since the reminder 305 ≠ 0, we apply division lemma to 168 and 305, to get

305 = 168 x 1 + 137

Step 3: We consider the new divisor 168 and the new remainder 137, and apply the division lemma to get

168 = 137 x 1 + 31

We consider the new divisor 137 and the new remainder 31,and apply the division lemma to get

137 = 31 x 4 + 13

We consider the new divisor 31 and the new remainder 13,and apply the division lemma to get

31 = 13 x 2 + 5

We consider the new divisor 13 and the new remainder 5,and apply the division lemma to get

13 = 5 x 2 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 778 and 305 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(13,5) = HCF(31,13) = HCF(137,31) = HCF(168,137) = HCF(305,168) = HCF(778,305) .

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

Step 1: Since 534 > 1, we apply the division lemma to 534 and 1, to get

534 = 1 x 534 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 534 is 1

Notice that 1 = HCF(534,1) .

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Frequently Asked Questions on HCF of 778, 305, 534 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, 305, 534?

Answer: HCF of 778, 305, 534 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 778, 305, 534 using Euclid's Algorithm?

Answer: For arbitrary numbers 778, 305, 534 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.