Highest Common Factor of 741, 676, 889 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 741, 676, 889 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 741, 676, 889 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 741, 676, 889 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 741, 676, 889 is 1.

HCF(741, 676, 889) = 1

HCF of 741, 676, 889 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 741, 676, 889 is 1.

Highest Common Factor of 741,676,889 using Euclid's algorithm

Highest Common Factor of 741,676,889 is 1

Step 1: Since 741 > 676, we apply the division lemma to 741 and 676, to get

741 = 676 x 1 + 65

Step 2: Since the reminder 676 ≠ 0, we apply division lemma to 65 and 676, to get

676 = 65 x 10 + 26

Step 3: We consider the new divisor 65 and the new remainder 26, and apply the division lemma to get

65 = 26 x 2 + 13

We consider the new divisor 26 and the new remainder 13, and apply the division lemma to get

26 = 13 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 13, the HCF of 741 and 676 is 13

Notice that 13 = HCF(26,13) = HCF(65,26) = HCF(676,65) = HCF(741,676) .

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

Step 1: Since 889 > 13, we apply the division lemma to 889 and 13, to get

889 = 13 x 68 + 5

Step 2: Since the reminder 13 ≠ 0, we apply division lemma to 5 and 13, to get

13 = 5 x 2 + 3

Step 3: We consider the new divisor 5 and the new remainder 3, and apply the division lemma to get

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 13 and 889 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(13,5) = HCF(889,13) .

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Frequently Asked Questions on HCF of 741, 676, 889 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 741, 676, 889?

Answer: HCF of 741, 676, 889 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 741, 676, 889 using Euclid's Algorithm?

Answer: For arbitrary numbers 741, 676, 889 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.