Highest Common Factor of 689, 888, 849 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 689, 888, 849 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 689, 888, 849 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 689, 888, 849 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 689, 888, 849 is 1.

HCF(689, 888, 849) = 1

HCF of 689, 888, 849 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 689, 888, 849 is 1.

Highest Common Factor of 689,888,849 using Euclid's algorithm

Highest Common Factor of 689,888,849 is 1

Step 1: Since 888 > 689, we apply the division lemma to 888 and 689, to get

888 = 689 x 1 + 199

Step 2: Since the reminder 689 ≠ 0, we apply division lemma to 199 and 689, to get

689 = 199 x 3 + 92

Step 3: We consider the new divisor 199 and the new remainder 92, and apply the division lemma to get

199 = 92 x 2 + 15

We consider the new divisor 92 and the new remainder 15,and apply the division lemma to get

92 = 15 x 6 + 2

We consider the new divisor 15 and the new remainder 2,and apply the division lemma to get

15 = 2 x 7 + 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 689 and 888 is 1

Notice that 1 = HCF(2,1) = HCF(15,2) = HCF(92,15) = HCF(199,92) = HCF(689,199) = HCF(888,689) .

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

Step 1: Since 849 > 1, we apply the division lemma to 849 and 1, to get

849 = 1 x 849 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 849 is 1

Notice that 1 = HCF(849,1) .

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Frequently Asked Questions on HCF of 689, 888, 849 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 689, 888, 849?

Answer: HCF of 689, 888, 849 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 689, 888, 849 using Euclid's Algorithm?

Answer: For arbitrary numbers 689, 888, 849 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.