Highest Common Factor of 972, 260, 623 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 972, 260, 623 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 972, 260, 623 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 972, 260, 623 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 972, 260, 623 is 1.

HCF(972, 260, 623) = 1

HCF of 972, 260, 623 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 972, 260, 623 is 1.

Highest Common Factor of 972,260,623 using Euclid's algorithm

Highest Common Factor of 972,260,623 is 1

Step 1: Since 972 > 260, we apply the division lemma to 972 and 260, to get

972 = 260 x 3 + 192

Step 2: Since the reminder 260 ≠ 0, we apply division lemma to 192 and 260, to get

260 = 192 x 1 + 68

Step 3: We consider the new divisor 192 and the new remainder 68, and apply the division lemma to get

192 = 68 x 2 + 56

We consider the new divisor 68 and the new remainder 56,and apply the division lemma to get

68 = 56 x 1 + 12

We consider the new divisor 56 and the new remainder 12,and apply the division lemma to get

56 = 12 x 4 + 8

We consider the new divisor 12 and the new remainder 8,and apply the division lemma to get

12 = 8 x 1 + 4

We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get

8 = 4 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 972 and 260 is 4

Notice that 4 = HCF(8,4) = HCF(12,8) = HCF(56,12) = HCF(68,56) = HCF(192,68) = HCF(260,192) = HCF(972,260) .

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

Step 1: Since 623 > 4, we apply the division lemma to 623 and 4, to get

623 = 4 x 155 + 3

Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 3 and 4, to get

4 = 3 x 1 + 1

Step 3: 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 4 and 623 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(623,4) .

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Frequently Asked Questions on HCF of 972, 260, 623 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 972, 260, 623?

Answer: HCF of 972, 260, 623 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 972, 260, 623 using Euclid's Algorithm?

Answer: For arbitrary numbers 972, 260, 623 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.