Highest Common Factor of 712, 977, 161 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 712, 977, 161 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 712, 977, 161 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 712, 977, 161 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 712, 977, 161 is 1.

HCF(712, 977, 161) = 1

HCF of 712, 977, 161 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 712, 977, 161 is 1.

Highest Common Factor of 712,977,161 using Euclid's algorithm

Highest Common Factor of 712,977,161 is 1

Step 1: Since 977 > 712, we apply the division lemma to 977 and 712, to get

977 = 712 x 1 + 265

Step 2: Since the reminder 712 ≠ 0, we apply division lemma to 265 and 712, to get

712 = 265 x 2 + 182

Step 3: We consider the new divisor 265 and the new remainder 182, and apply the division lemma to get

265 = 182 x 1 + 83

We consider the new divisor 182 and the new remainder 83,and apply the division lemma to get

182 = 83 x 2 + 16

We consider the new divisor 83 and the new remainder 16,and apply the division lemma to get

83 = 16 x 5 + 3

We consider the new divisor 16 and the new remainder 3,and apply the division lemma to get

16 = 3 x 5 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 712 and 977 is 1

Notice that 1 = HCF(3,1) = HCF(16,3) = HCF(83,16) = HCF(182,83) = HCF(265,182) = HCF(712,265) = HCF(977,712) .

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

Step 1: Since 161 > 1, we apply the division lemma to 161 and 1, to get

161 = 1 x 161 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 161 is 1

Notice that 1 = HCF(161,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 712, 977, 161 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 712, 977, 161?

Answer: HCF of 712, 977, 161 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 712, 977, 161 using Euclid's Algorithm?

Answer: For arbitrary numbers 712, 977, 161 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.