Highest Common Factor of 698, 890, 199 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 698, 890, 199 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 698, 890, 199 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 698, 890, 199 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 698, 890, 199 is 1.

HCF(698, 890, 199) = 1

HCF of 698, 890, 199 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 698, 890, 199 is 1.

Highest Common Factor of 698,890,199 using Euclid's algorithm

Highest Common Factor of 698,890,199 is 1

Step 1: Since 890 > 698, we apply the division lemma to 890 and 698, to get

890 = 698 x 1 + 192

Step 2: Since the reminder 698 ≠ 0, we apply division lemma to 192 and 698, to get

698 = 192 x 3 + 122

Step 3: We consider the new divisor 192 and the new remainder 122, and apply the division lemma to get

192 = 122 x 1 + 70

We consider the new divisor 122 and the new remainder 70,and apply the division lemma to get

122 = 70 x 1 + 52

We consider the new divisor 70 and the new remainder 52,and apply the division lemma to get

70 = 52 x 1 + 18

We consider the new divisor 52 and the new remainder 18,and apply the division lemma to get

52 = 18 x 2 + 16

We consider the new divisor 18 and the new remainder 16,and apply the division lemma to get

18 = 16 x 1 + 2

We consider the new divisor 16 and the new remainder 2,and apply the division lemma to get

16 = 2 x 8 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 698 and 890 is 2

Notice that 2 = HCF(16,2) = HCF(18,16) = HCF(52,18) = HCF(70,52) = HCF(122,70) = HCF(192,122) = HCF(698,192) = HCF(890,698) .

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

Step 1: Since 199 > 2, we apply the division lemma to 199 and 2, to get

199 = 2 x 99 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 199 is 1

Notice that 1 = HCF(2,1) = HCF(199,2) .

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Frequently Asked Questions on HCF of 698, 890, 199 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 698, 890, 199?

Answer: HCF of 698, 890, 199 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 698, 890, 199 using Euclid's Algorithm?

Answer: For arbitrary numbers 698, 890, 199 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.