Highest Common Factor of 712, 975, 164 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, 975, 164 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 712, 975, 164 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, 975, 164 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, 975, 164 is 1.

HCF(712, 975, 164) = 1

HCF of 712, 975, 164 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, 975, 164 is 1.

Highest Common Factor of 712,975,164 using Euclid's algorithm

Highest Common Factor of 712,975,164 is 1

Step 1: Since 975 > 712, we apply the division lemma to 975 and 712, to get

975 = 712 x 1 + 263

Step 2: Since the reminder 712 ≠ 0, we apply division lemma to 263 and 712, to get

712 = 263 x 2 + 186

Step 3: We consider the new divisor 263 and the new remainder 186, and apply the division lemma to get

263 = 186 x 1 + 77

We consider the new divisor 186 and the new remainder 77,and apply the division lemma to get

186 = 77 x 2 + 32

We consider the new divisor 77 and the new remainder 32,and apply the division lemma to get

77 = 32 x 2 + 13

We consider the new divisor 32 and the new remainder 13,and apply the division lemma to get

32 = 13 x 2 + 6

We consider the new divisor 13 and the new remainder 6,and apply the division lemma to get

13 = 6 x 2 + 1

We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get

6 = 1 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 712 and 975 is 1

Notice that 1 = HCF(6,1) = HCF(13,6) = HCF(32,13) = HCF(77,32) = HCF(186,77) = HCF(263,186) = HCF(712,263) = HCF(975,712) .

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

Step 1: Since 164 > 1, we apply the division lemma to 164 and 1, to get

164 = 1 x 164 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 164 is 1

Notice that 1 = HCF(164,1) .

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Frequently Asked Questions on HCF of 712, 975, 164 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, 975, 164?

Answer: HCF of 712, 975, 164 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 712, 975, 164 using Euclid's Algorithm?

Answer: For arbitrary numbers 712, 975, 164 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.