Highest Common Factor of 785, 974, 212 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 785, 974, 212 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 785, 974, 212 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 785, 974, 212 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 785, 974, 212 is 1.

HCF(785, 974, 212) = 1

HCF of 785, 974, 212 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 785, 974, 212 is 1.

Highest Common Factor of 785,974,212 using Euclid's algorithm

Highest Common Factor of 785,974,212 is 1

Step 1: Since 974 > 785, we apply the division lemma to 974 and 785, to get

974 = 785 x 1 + 189

Step 2: Since the reminder 785 ≠ 0, we apply division lemma to 189 and 785, to get

785 = 189 x 4 + 29

Step 3: We consider the new divisor 189 and the new remainder 29, and apply the division lemma to get

189 = 29 x 6 + 15

We consider the new divisor 29 and the new remainder 15,and apply the division lemma to get

29 = 15 x 1 + 14

We consider the new divisor 15 and the new remainder 14,and apply the division lemma to get

15 = 14 x 1 + 1

We consider the new divisor 14 and the new remainder 1,and apply the division lemma to get

14 = 1 x 14 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 785 and 974 is 1

Notice that 1 = HCF(14,1) = HCF(15,14) = HCF(29,15) = HCF(189,29) = HCF(785,189) = HCF(974,785) .

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

Step 1: Since 212 > 1, we apply the division lemma to 212 and 1, to get

212 = 1 x 212 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 212 is 1

Notice that 1 = HCF(212,1) .

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Frequently Asked Questions on HCF of 785, 974, 212 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 785, 974, 212?

Answer: HCF of 785, 974, 212 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 785, 974, 212 using Euclid's Algorithm?

Answer: For arbitrary numbers 785, 974, 212 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.