Highest Common Factor of 698, 989, 660 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, 989, 660 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 698, 989, 660 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, 989, 660 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, 989, 660 is 1.

HCF(698, 989, 660) = 1

HCF of 698, 989, 660 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, 989, 660 is 1.

Highest Common Factor of 698,989,660 using Euclid's algorithm

Highest Common Factor of 698,989,660 is 1

Step 1: Since 989 > 698, we apply the division lemma to 989 and 698, to get

989 = 698 x 1 + 291

Step 2: Since the reminder 698 ≠ 0, we apply division lemma to 291 and 698, to get

698 = 291 x 2 + 116

Step 3: We consider the new divisor 291 and the new remainder 116, and apply the division lemma to get

291 = 116 x 2 + 59

We consider the new divisor 116 and the new remainder 59,and apply the division lemma to get

116 = 59 x 1 + 57

We consider the new divisor 59 and the new remainder 57,and apply the division lemma to get

59 = 57 x 1 + 2

We consider the new divisor 57 and the new remainder 2,and apply the division lemma to get

57 = 2 x 28 + 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 698 and 989 is 1

Notice that 1 = HCF(2,1) = HCF(57,2) = HCF(59,57) = HCF(116,59) = HCF(291,116) = HCF(698,291) = HCF(989,698) .

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

Step 1: Since 660 > 1, we apply the division lemma to 660 and 1, to get

660 = 1 x 660 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 660 is 1

Notice that 1 = HCF(660,1) .

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Frequently Asked Questions on HCF of 698, 989, 660 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, 989, 660?

Answer: HCF of 698, 989, 660 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 698, 989, 660 using Euclid's Algorithm?

Answer: For arbitrary numbers 698, 989, 660 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.