Highest Common Factor of 864, 553, 752 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 864, 553, 752 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 864, 553, 752 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 864, 553, 752 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 864, 553, 752 is 1.

HCF(864, 553, 752) = 1

HCF of 864, 553, 752 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 864, 553, 752 is 1.

Highest Common Factor of 864,553,752 using Euclid's algorithm

Highest Common Factor of 864,553,752 is 1

Step 1: Since 864 > 553, we apply the division lemma to 864 and 553, to get

864 = 553 x 1 + 311

Step 2: Since the reminder 553 ≠ 0, we apply division lemma to 311 and 553, to get

553 = 311 x 1 + 242

Step 3: We consider the new divisor 311 and the new remainder 242, and apply the division lemma to get

311 = 242 x 1 + 69

We consider the new divisor 242 and the new remainder 69,and apply the division lemma to get

242 = 69 x 3 + 35

We consider the new divisor 69 and the new remainder 35,and apply the division lemma to get

69 = 35 x 1 + 34

We consider the new divisor 35 and the new remainder 34,and apply the division lemma to get

35 = 34 x 1 + 1

We consider the new divisor 34 and the new remainder 1,and apply the division lemma to get

34 = 1 x 34 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 864 and 553 is 1

Notice that 1 = HCF(34,1) = HCF(35,34) = HCF(69,35) = HCF(242,69) = HCF(311,242) = HCF(553,311) = HCF(864,553) .

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

Step 1: Since 752 > 1, we apply the division lemma to 752 and 1, to get

752 = 1 x 752 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 752 is 1

Notice that 1 = HCF(752,1) .

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Frequently Asked Questions on HCF of 864, 553, 752 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 864, 553, 752?

Answer: HCF of 864, 553, 752 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 864, 553, 752 using Euclid's Algorithm?

Answer: For arbitrary numbers 864, 553, 752 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.