Highest Common Factor of 547, 900, 774 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 547, 900, 774 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 547, 900, 774 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 547, 900, 774 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 547, 900, 774 is 1.

HCF(547, 900, 774) = 1

HCF of 547, 900, 774 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 547, 900, 774 is 1.

Highest Common Factor of 547,900,774 using Euclid's algorithm

Highest Common Factor of 547,900,774 is 1

Step 1: Since 900 > 547, we apply the division lemma to 900 and 547, to get

900 = 547 x 1 + 353

Step 2: Since the reminder 547 ≠ 0, we apply division lemma to 353 and 547, to get

547 = 353 x 1 + 194

Step 3: We consider the new divisor 353 and the new remainder 194, and apply the division lemma to get

353 = 194 x 1 + 159

We consider the new divisor 194 and the new remainder 159,and apply the division lemma to get

194 = 159 x 1 + 35

We consider the new divisor 159 and the new remainder 35,and apply the division lemma to get

159 = 35 x 4 + 19

We consider the new divisor 35 and the new remainder 19,and apply the division lemma to get

35 = 19 x 1 + 16

We consider the new divisor 19 and the new remainder 16,and apply the division lemma to get

19 = 16 x 1 + 3

We consider the new divisor 16 and the new remainder 3,and apply the division lemma to get

16 = 3 x 5 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 547 and 900 is 1

Notice that 1 = HCF(3,1) = HCF(16,3) = HCF(19,16) = HCF(35,19) = HCF(159,35) = HCF(194,159) = HCF(353,194) = HCF(547,353) = HCF(900,547) .

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

Step 1: Since 774 > 1, we apply the division lemma to 774 and 1, to get

774 = 1 x 774 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 774 is 1

Notice that 1 = HCF(774,1) .

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Frequently Asked Questions on HCF of 547, 900, 774 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 547, 900, 774?

Answer: HCF of 547, 900, 774 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 547, 900, 774 using Euclid's Algorithm?

Answer: For arbitrary numbers 547, 900, 774 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.