Highest Common Factor of 754, 591, 512, 85 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 754, 591, 512, 85 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 754, 591, 512, 85 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 754, 591, 512, 85 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 754, 591, 512, 85 is 1.

HCF(754, 591, 512, 85) = 1

HCF of 754, 591, 512, 85 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 754, 591, 512, 85 is 1.

Highest Common Factor of 754,591,512,85 using Euclid's algorithm

Highest Common Factor of 754,591,512,85 is 1

Step 1: Since 754 > 591, we apply the division lemma to 754 and 591, to get

754 = 591 x 1 + 163

Step 2: Since the reminder 591 ≠ 0, we apply division lemma to 163 and 591, to get

591 = 163 x 3 + 102

Step 3: We consider the new divisor 163 and the new remainder 102, and apply the division lemma to get

163 = 102 x 1 + 61

We consider the new divisor 102 and the new remainder 61,and apply the division lemma to get

102 = 61 x 1 + 41

We consider the new divisor 61 and the new remainder 41,and apply the division lemma to get

61 = 41 x 1 + 20

We consider the new divisor 41 and the new remainder 20,and apply the division lemma to get

41 = 20 x 2 + 1

We consider the new divisor 20 and the new remainder 1,and apply the division lemma to get

20 = 1 x 20 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 754 and 591 is 1

Notice that 1 = HCF(20,1) = HCF(41,20) = HCF(61,41) = HCF(102,61) = HCF(163,102) = HCF(591,163) = HCF(754,591) .

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

Step 1: Since 512 > 1, we apply the division lemma to 512 and 1, to get

512 = 1 x 512 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 512 is 1

Notice that 1 = HCF(512,1) .

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

Step 1: Since 85 > 1, we apply the division lemma to 85 and 1, to get

85 = 1 x 85 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 85 is 1

Notice that 1 = HCF(85,1) .

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Frequently Asked Questions on HCF of 754, 591, 512, 85 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 754, 591, 512, 85?

Answer: HCF of 754, 591, 512, 85 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 754, 591, 512, 85 using Euclid's Algorithm?

Answer: For arbitrary numbers 754, 591, 512, 85 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.