Highest Common Factor of 497, 804, 577 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 497, 804, 577 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 497, 804, 577 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 497, 804, 577 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 497, 804, 577 is 1.

HCF(497, 804, 577) = 1

HCF of 497, 804, 577 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 497, 804, 577 is 1.

Highest Common Factor of 497,804,577 using Euclid's algorithm

Highest Common Factor of 497,804,577 is 1

Step 1: Since 804 > 497, we apply the division lemma to 804 and 497, to get

804 = 497 x 1 + 307

Step 2: Since the reminder 497 ≠ 0, we apply division lemma to 307 and 497, to get

497 = 307 x 1 + 190

Step 3: We consider the new divisor 307 and the new remainder 190, and apply the division lemma to get

307 = 190 x 1 + 117

We consider the new divisor 190 and the new remainder 117,and apply the division lemma to get

190 = 117 x 1 + 73

We consider the new divisor 117 and the new remainder 73,and apply the division lemma to get

117 = 73 x 1 + 44

We consider the new divisor 73 and the new remainder 44,and apply the division lemma to get

73 = 44 x 1 + 29

We consider the new divisor 44 and the new remainder 29,and apply the division lemma to get

44 = 29 x 1 + 15

We consider the new divisor 29 and the new remainder 15,and apply the division lemma to get

29 = 15 x 1 + 14

We consider the new divisor 15 and the new remainder 14,and apply the division lemma to get

15 = 14 x 1 + 1

We consider the new divisor 14 and the new remainder 1,and apply the division lemma to get

14 = 1 x 14 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 497 and 804 is 1

Notice that 1 = HCF(14,1) = HCF(15,14) = HCF(29,15) = HCF(44,29) = HCF(73,44) = HCF(117,73) = HCF(190,117) = HCF(307,190) = HCF(497,307) = HCF(804,497) .

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

Step 1: Since 577 > 1, we apply the division lemma to 577 and 1, to get

577 = 1 x 577 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 577 is 1

Notice that 1 = HCF(577,1) .

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Frequently Asked Questions on HCF of 497, 804, 577 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 497, 804, 577?

Answer: HCF of 497, 804, 577 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 497, 804, 577 using Euclid's Algorithm?

Answer: For arbitrary numbers 497, 804, 577 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.