Highest Common Factor of 985, 2818, 6974 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 985, 2818, 6974 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 985, 2818, 6974 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 985, 2818, 6974 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 985, 2818, 6974 is 1.

HCF(985, 2818, 6974) = 1

HCF of 985, 2818, 6974 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 985, 2818, 6974 is 1.

Highest Common Factor of 985,2818,6974 using Euclid's algorithm

Highest Common Factor of 985,2818,6974 is 1

Step 1: Since 2818 > 985, we apply the division lemma to 2818 and 985, to get

2818 = 985 x 2 + 848

Step 2: Since the reminder 985 ≠ 0, we apply division lemma to 848 and 985, to get

985 = 848 x 1 + 137

Step 3: We consider the new divisor 848 and the new remainder 137, and apply the division lemma to get

848 = 137 x 6 + 26

We consider the new divisor 137 and the new remainder 26,and apply the division lemma to get

137 = 26 x 5 + 7

We consider the new divisor 26 and the new remainder 7,and apply the division lemma to get

26 = 7 x 3 + 5

We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get

7 = 5 x 1 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 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 985 and 2818 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(26,7) = HCF(137,26) = HCF(848,137) = HCF(985,848) = HCF(2818,985) .

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

Step 1: Since 6974 > 1, we apply the division lemma to 6974 and 1, to get

6974 = 1 x 6974 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 6974 is 1

Notice that 1 = HCF(6974,1) .

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Frequently Asked Questions on HCF of 985, 2818, 6974 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 985, 2818, 6974?

Answer: HCF of 985, 2818, 6974 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 985, 2818, 6974 using Euclid's Algorithm?

Answer: For arbitrary numbers 985, 2818, 6974 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.