Highest Common Factor of 804, 492, 277 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 804, 492, 277 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 804, 492, 277 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 804, 492, 277 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 804, 492, 277 is 1.

HCF(804, 492, 277) = 1

HCF of 804, 492, 277 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 804, 492, 277 is 1.

Highest Common Factor of 804,492,277 using Euclid's algorithm

Highest Common Factor of 804,492,277 is 1

Step 1: Since 804 > 492, we apply the division lemma to 804 and 492, to get

804 = 492 x 1 + 312

Step 2: Since the reminder 492 ≠ 0, we apply division lemma to 312 and 492, to get

492 = 312 x 1 + 180

Step 3: We consider the new divisor 312 and the new remainder 180, and apply the division lemma to get

312 = 180 x 1 + 132

We consider the new divisor 180 and the new remainder 132,and apply the division lemma to get

180 = 132 x 1 + 48

We consider the new divisor 132 and the new remainder 48,and apply the division lemma to get

132 = 48 x 2 + 36

We consider the new divisor 48 and the new remainder 36,and apply the division lemma to get

48 = 36 x 1 + 12

We consider the new divisor 36 and the new remainder 12,and apply the division lemma to get

36 = 12 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 804 and 492 is 12

Notice that 12 = HCF(36,12) = HCF(48,36) = HCF(132,48) = HCF(180,132) = HCF(312,180) = HCF(492,312) = HCF(804,492) .

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

Step 1: Since 277 > 12, we apply the division lemma to 277 and 12, to get

277 = 12 x 23 + 1

Step 2: Since the reminder 12 ≠ 0, we apply division lemma to 1 and 12, to get

12 = 1 x 12 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 12 and 277 is 1

Notice that 1 = HCF(12,1) = HCF(277,12) .

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Frequently Asked Questions on HCF of 804, 492, 277 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 804, 492, 277?

Answer: HCF of 804, 492, 277 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 804, 492, 277 using Euclid's Algorithm?

Answer: For arbitrary numbers 804, 492, 277 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.