Highest Common Factor of 505, 846, 318 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, 846, 318 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 505, 846, 318 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, 846, 318 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, 846, 318 is 1.

HCF(505, 846, 318) = 1

HCF of 505, 846, 318 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, 846, 318 is 1.

Highest Common Factor of 505,846,318 using Euclid's algorithm

Highest Common Factor of 505,846,318 is 1

Step 1: Since 846 > 505, we apply the division lemma to 846 and 505, to get

846 = 505 x 1 + 341

Step 2: Since the reminder 505 ≠ 0, we apply division lemma to 341 and 505, to get

505 = 341 x 1 + 164

Step 3: We consider the new divisor 341 and the new remainder 164, and apply the division lemma to get

341 = 164 x 2 + 13

We consider the new divisor 164 and the new remainder 13,and apply the division lemma to get

164 = 13 x 12 + 8

We consider the new divisor 13 and the new remainder 8,and apply the division lemma to get

13 = 8 x 1 + 5

We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get

8 = 5 x 1 + 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 505 and 846 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(13,8) = HCF(164,13) = HCF(341,164) = HCF(505,341) = HCF(846,505) .

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

Step 1: Since 318 > 1, we apply the division lemma to 318 and 1, to get

318 = 1 x 318 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 318 is 1

Notice that 1 = HCF(318,1) .

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Frequently Asked Questions on HCF of 505, 846, 318 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, 846, 318?

Answer: HCF of 505, 846, 318 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 505, 846, 318 using Euclid's Algorithm?

Answer: For arbitrary numbers 505, 846, 318 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.