Highest Common Factor of 778, 602, 622 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, 602, 622 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 778, 602, 622 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 778, 602, 622 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, 602, 622 is 2.

HCF(778, 602, 622) = 2

HCF of 778, 602, 622 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, 602, 622 is 2.

Highest Common Factor of 778,602,622 using Euclid's algorithm

Highest Common Factor of 778,602,622 is 2

Step 1: Since 778 > 602, we apply the division lemma to 778 and 602, to get

778 = 602 x 1 + 176

Step 2: Since the reminder 602 ≠ 0, we apply division lemma to 176 and 602, to get

602 = 176 x 3 + 74

Step 3: We consider the new divisor 176 and the new remainder 74, and apply the division lemma to get

176 = 74 x 2 + 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 778 and 602 is 2

Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(18,10) = HCF(28,18) = HCF(74,28) = HCF(176,74) = HCF(602,176) = HCF(778,602) .

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

Step 1: Since 622 > 2, we apply the division lemma to 622 and 2, to get

622 = 2 x 311 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 622 is 2

Notice that 2 = HCF(622,2) .

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Frequently Asked Questions on HCF of 778, 602, 622 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, 602, 622?

Answer: HCF of 778, 602, 622 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 778, 602, 622 using Euclid's Algorithm?

Answer: For arbitrary numbers 778, 602, 622 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.