Highest Common Factor of 168, 779, 972 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 168, 779, 972 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 168, 779, 972 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 168, 779, 972 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 168, 779, 972 is 1.

HCF(168, 779, 972) = 1

HCF of 168, 779, 972 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 168, 779, 972 is 1.

Highest Common Factor of 168,779,972 using Euclid's algorithm

Highest Common Factor of 168,779,972 is 1

Step 1: Since 779 > 168, we apply the division lemma to 779 and 168, to get

779 = 168 x 4 + 107

Step 2: Since the reminder 168 ≠ 0, we apply division lemma to 107 and 168, to get

168 = 107 x 1 + 61

Step 3: We consider the new divisor 107 and the new remainder 61, and apply the division lemma to get

107 = 61 x 1 + 46

We consider the new divisor 61 and the new remainder 46,and apply the division lemma to get

61 = 46 x 1 + 15

We consider the new divisor 46 and the new remainder 15,and apply the division lemma to get

46 = 15 x 3 + 1

We consider the new divisor 15 and the new remainder 1,and apply the division lemma to get

15 = 1 x 15 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 168 and 779 is 1

Notice that 1 = HCF(15,1) = HCF(46,15) = HCF(61,46) = HCF(107,61) = HCF(168,107) = HCF(779,168) .

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

Step 1: Since 972 > 1, we apply the division lemma to 972 and 1, to get

972 = 1 x 972 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 972 is 1

Notice that 1 = HCF(972,1) .

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Frequently Asked Questions on HCF of 168, 779, 972 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 168, 779, 972?

Answer: HCF of 168, 779, 972 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 168, 779, 972 using Euclid's Algorithm?

Answer: For arbitrary numbers 168, 779, 972 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.