Highest Common Factor of 698, 512, 735 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 698, 512, 735 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 698, 512, 735 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 698, 512, 735 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 698, 512, 735 is 1.

HCF(698, 512, 735) = 1

HCF of 698, 512, 735 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 698, 512, 735 is 1.

Highest Common Factor of 698,512,735 using Euclid's algorithm

Highest Common Factor of 698,512,735 is 1

Step 1: Since 698 > 512, we apply the division lemma to 698 and 512, to get

698 = 512 x 1 + 186

Step 2: Since the reminder 512 ≠ 0, we apply division lemma to 186 and 512, to get

512 = 186 x 2 + 140

Step 3: We consider the new divisor 186 and the new remainder 140, and apply the division lemma to get

186 = 140 x 1 + 46

We consider the new divisor 140 and the new remainder 46,and apply the division lemma to get

140 = 46 x 3 + 2

We consider the new divisor 46 and the new remainder 2,and apply the division lemma to get

46 = 2 x 23 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 698 and 512 is 2

Notice that 2 = HCF(46,2) = HCF(140,46) = HCF(186,140) = HCF(512,186) = HCF(698,512) .

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

Step 1: Since 735 > 2, we apply the division lemma to 735 and 2, to get

735 = 2 x 367 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 735 is 1

Notice that 1 = HCF(2,1) = HCF(735,2) .

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Frequently Asked Questions on HCF of 698, 512, 735 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 698, 512, 735?

Answer: HCF of 698, 512, 735 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 698, 512, 735 using Euclid's Algorithm?

Answer: For arbitrary numbers 698, 512, 735 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.