Highest Common Factor of 781, 299, 222 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 781, 299, 222 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 781, 299, 222 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 781, 299, 222 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 781, 299, 222 is 1.

HCF(781, 299, 222) = 1

HCF of 781, 299, 222 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 781, 299, 222 is 1.

Highest Common Factor of 781,299,222 using Euclid's algorithm

Highest Common Factor of 781,299,222 is 1

Step 1: Since 781 > 299, we apply the division lemma to 781 and 299, to get

781 = 299 x 2 + 183

Step 2: Since the reminder 299 ≠ 0, we apply division lemma to 183 and 299, to get

299 = 183 x 1 + 116

Step 3: We consider the new divisor 183 and the new remainder 116, and apply the division lemma to get

183 = 116 x 1 + 67

We consider the new divisor 116 and the new remainder 67,and apply the division lemma to get

116 = 67 x 1 + 49

We consider the new divisor 67 and the new remainder 49,and apply the division lemma to get

67 = 49 x 1 + 18

We consider the new divisor 49 and the new remainder 18,and apply the division lemma to get

49 = 18 x 2 + 13

We consider the new divisor 18 and the new remainder 13,and apply the division lemma to get

18 = 13 x 1 + 5

We consider the new divisor 13 and the new remainder 5,and apply the division lemma to get

13 = 5 x 2 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 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 781 and 299 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(13,5) = HCF(18,13) = HCF(49,18) = HCF(67,49) = HCF(116,67) = HCF(183,116) = HCF(299,183) = HCF(781,299) .

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

Step 1: Since 222 > 1, we apply the division lemma to 222 and 1, to get

222 = 1 x 222 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 222 is 1

Notice that 1 = HCF(222,1) .

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Frequently Asked Questions on HCF of 781, 299, 222 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 781, 299, 222?

Answer: HCF of 781, 299, 222 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 781, 299, 222 using Euclid's Algorithm?

Answer: For arbitrary numbers 781, 299, 222 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.