Highest Common Factor of 552, 770, 814 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 552, 770, 814 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 552, 770, 814 is 2 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 552, 770, 814 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 552, 770, 814 is 2.

HCF(552, 770, 814) = 2

HCF of 552, 770, 814 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 552, 770, 814 is 2.

Highest Common Factor of 552,770,814 using Euclid's algorithm

Highest Common Factor of 552,770,814 is 2

Step 1: Since 770 > 552, we apply the division lemma to 770 and 552, to get

770 = 552 x 1 + 218

Step 2: Since the reminder 552 ≠ 0, we apply division lemma to 218 and 552, to get

552 = 218 x 2 + 116

Step 3: We consider the new divisor 218 and the new remainder 116, and apply the division lemma to get

218 = 116 x 1 + 102

We consider the new divisor 116 and the new remainder 102,and apply the division lemma to get

116 = 102 x 1 + 14

We consider the new divisor 102 and the new remainder 14,and apply the division lemma to get

102 = 14 x 7 + 4

We consider the new divisor 14 and the new remainder 4,and apply the division lemma to get

14 = 4 x 3 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 552 and 770 is 2

Notice that 2 = HCF(4,2) = HCF(14,4) = HCF(102,14) = HCF(116,102) = HCF(218,116) = HCF(552,218) = HCF(770,552) .

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

Step 1: Since 814 > 2, we apply the division lemma to 814 and 2, to get

814 = 2 x 407 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 814 is 2

Notice that 2 = HCF(814,2) .

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Frequently Asked Questions on HCF of 552, 770, 814 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 552, 770, 814?

Answer: HCF of 552, 770, 814 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 552, 770, 814 using Euclid's Algorithm?

Answer: For arbitrary numbers 552, 770, 814 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.