Highest Common Factor of 356, 546, 503 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 356, 546, 503 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 356, 546, 503 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 356, 546, 503 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 356, 546, 503 is 1.

HCF(356, 546, 503) = 1

HCF of 356, 546, 503 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 356, 546, 503 is 1.

Highest Common Factor of 356,546,503 using Euclid's algorithm

Highest Common Factor of 356,546,503 is 1

Step 1: Since 546 > 356, we apply the division lemma to 546 and 356, to get

546 = 356 x 1 + 190

Step 2: Since the reminder 356 ≠ 0, we apply division lemma to 190 and 356, to get

356 = 190 x 1 + 166

Step 3: We consider the new divisor 190 and the new remainder 166, and apply the division lemma to get

190 = 166 x 1 + 24

We consider the new divisor 166 and the new remainder 24,and apply the division lemma to get

166 = 24 x 6 + 22

We consider the new divisor 24 and the new remainder 22,and apply the division lemma to get

24 = 22 x 1 + 2

We consider the new divisor 22 and the new remainder 2,and apply the division lemma to get

22 = 2 x 11 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 356 and 546 is 2

Notice that 2 = HCF(22,2) = HCF(24,22) = HCF(166,24) = HCF(190,166) = HCF(356,190) = HCF(546,356) .

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

Step 1: Since 503 > 2, we apply the division lemma to 503 and 2, to get

503 = 2 x 251 + 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 503 is 1

Notice that 1 = HCF(2,1) = HCF(503,2) .

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Frequently Asked Questions on HCF of 356, 546, 503 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 356, 546, 503?

Answer: HCF of 356, 546, 503 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 356, 546, 503 using Euclid's Algorithm?

Answer: For arbitrary numbers 356, 546, 503 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.