Highest Common Factor of 505, 868, 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 505, 868, 622 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 505, 868, 622 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 505, 868, 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 505, 868, 622 is 1.

HCF(505, 868, 622) = 1

HCF of 505, 868, 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 505, 868, 622 is 1.

Highest Common Factor of 505,868,622 using Euclid's algorithm

Highest Common Factor of 505,868,622 is 1

Step 1: Since 868 > 505, we apply the division lemma to 868 and 505, to get

868 = 505 x 1 + 363

Step 2: Since the reminder 505 ≠ 0, we apply division lemma to 363 and 505, to get

505 = 363 x 1 + 142

Step 3: We consider the new divisor 363 and the new remainder 142, and apply the division lemma to get

363 = 142 x 2 + 79

We consider the new divisor 142 and the new remainder 79,and apply the division lemma to get

142 = 79 x 1 + 63

We consider the new divisor 79 and the new remainder 63,and apply the division lemma to get

79 = 63 x 1 + 16

We consider the new divisor 63 and the new remainder 16,and apply the division lemma to get

63 = 16 x 3 + 15

We consider the new divisor 16 and the new remainder 15,and apply the division lemma to get

16 = 15 x 1 + 1

We consider the new divisor 15 and the new remainder 1,and apply the division lemma to get

15 = 1 x 15 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 505 and 868 is 1

Notice that 1 = HCF(15,1) = HCF(16,15) = HCF(63,16) = HCF(79,63) = HCF(142,79) = HCF(363,142) = HCF(505,363) = HCF(868,505) .

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

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

622 = 1 x 622 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 622 is 1

Notice that 1 = HCF(622,1) .

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Frequently Asked Questions on HCF of 505, 868, 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 505, 868, 622?

Answer: HCF of 505, 868, 622 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 505, 868, 622 using Euclid's Algorithm?

Answer: For arbitrary numbers 505, 868, 622 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.