Highest Common Factor of 772, 561, 160 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 772, 561, 160 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 772, 561, 160 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 772, 561, 160 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 772, 561, 160 is 1.

HCF(772, 561, 160) = 1

HCF of 772, 561, 160 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 772, 561, 160 is 1.

Highest Common Factor of 772,561,160 using Euclid's algorithm

Highest Common Factor of 772,561,160 is 1

Step 1: Since 772 > 561, we apply the division lemma to 772 and 561, to get

772 = 561 x 1 + 211

Step 2: Since the reminder 561 ≠ 0, we apply division lemma to 211 and 561, to get

561 = 211 x 2 + 139

Step 3: We consider the new divisor 211 and the new remainder 139, and apply the division lemma to get

211 = 139 x 1 + 72

We consider the new divisor 139 and the new remainder 72,and apply the division lemma to get

139 = 72 x 1 + 67

We consider the new divisor 72 and the new remainder 67,and apply the division lemma to get

72 = 67 x 1 + 5

We consider the new divisor 67 and the new remainder 5,and apply the division lemma to get

67 = 5 x 13 + 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 772 and 561 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(67,5) = HCF(72,67) = HCF(139,72) = HCF(211,139) = HCF(561,211) = HCF(772,561) .

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

Step 1: Since 160 > 1, we apply the division lemma to 160 and 1, to get

160 = 1 x 160 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 160 is 1

Notice that 1 = HCF(160,1) .

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Frequently Asked Questions on HCF of 772, 561, 160 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 772, 561, 160?

Answer: HCF of 772, 561, 160 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 772, 561, 160 using Euclid's Algorithm?

Answer: For arbitrary numbers 772, 561, 160 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.