Highest Common Factor of 898, 6989, 6570 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 898, 6989, 6570 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 898, 6989, 6570 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 898, 6989, 6570 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 898, 6989, 6570 is 1.

HCF(898, 6989, 6570) = 1

HCF of 898, 6989, 6570 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 898, 6989, 6570 is 1.

Highest Common Factor of 898,6989,6570 using Euclid's algorithm

Highest Common Factor of 898,6989,6570 is 1

Step 1: Since 6989 > 898, we apply the division lemma to 6989 and 898, to get

6989 = 898 x 7 + 703

Step 2: Since the reminder 898 ≠ 0, we apply division lemma to 703 and 898, to get

898 = 703 x 1 + 195

Step 3: We consider the new divisor 703 and the new remainder 195, and apply the division lemma to get

703 = 195 x 3 + 118

We consider the new divisor 195 and the new remainder 118,and apply the division lemma to get

195 = 118 x 1 + 77

We consider the new divisor 118 and the new remainder 77,and apply the division lemma to get

118 = 77 x 1 + 41

We consider the new divisor 77 and the new remainder 41,and apply the division lemma to get

77 = 41 x 1 + 36

We consider the new divisor 41 and the new remainder 36,and apply the division lemma to get

41 = 36 x 1 + 5

We consider the new divisor 36 and the new remainder 5,and apply the division lemma to get

36 = 5 x 7 + 1

We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 898 and 6989 is 1

Notice that 1 = HCF(5,1) = HCF(36,5) = HCF(41,36) = HCF(77,41) = HCF(118,77) = HCF(195,118) = HCF(703,195) = HCF(898,703) = HCF(6989,898) .

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

Step 1: Since 6570 > 1, we apply the division lemma to 6570 and 1, to get

6570 = 1 x 6570 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 6570 is 1

Notice that 1 = HCF(6570,1) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 898, 6989, 6570 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 898, 6989, 6570?

Answer: HCF of 898, 6989, 6570 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 898, 6989, 6570 using Euclid's Algorithm?

Answer: For arbitrary numbers 898, 6989, 6570 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.