Highest Common Factor of 68, 996, 975 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 68, 996, 975 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 68, 996, 975 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 68, 996, 975 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 68, 996, 975 is 1.

HCF(68, 996, 975) = 1

HCF of 68, 996, 975 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 68, 996, 975 is 1.

Highest Common Factor of 68,996,975 using Euclid's algorithm

Highest Common Factor of 68,996,975 is 1

Step 1: Since 996 > 68, we apply the division lemma to 996 and 68, to get

996 = 68 x 14 + 44

Step 2: Since the reminder 68 ≠ 0, we apply division lemma to 44 and 68, to get

68 = 44 x 1 + 24

Step 3: We consider the new divisor 44 and the new remainder 24, and apply the division lemma to get

44 = 24 x 1 + 20

We consider the new divisor 24 and the new remainder 20,and apply the division lemma to get

24 = 20 x 1 + 4

We consider the new divisor 20 and the new remainder 4,and apply the division lemma to get

20 = 4 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 68 and 996 is 4

Notice that 4 = HCF(20,4) = HCF(24,20) = HCF(44,24) = HCF(68,44) = HCF(996,68) .

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

Step 1: Since 975 > 4, we apply the division lemma to 975 and 4, to get

975 = 4 x 243 + 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 975 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(975,4) .

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Frequently Asked Questions on HCF of 68, 996, 975 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 68, 996, 975?

Answer: HCF of 68, 996, 975 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 68, 996, 975 using Euclid's Algorithm?

Answer: For arbitrary numbers 68, 996, 975 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.