Highest Common Factor of 675, 429, 698 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 675, 429, 698 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 675, 429, 698 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 675, 429, 698 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 675, 429, 698 is 1.

HCF(675, 429, 698) = 1

HCF of 675, 429, 698 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 675, 429, 698 is 1.

Highest Common Factor of 675,429,698 using Euclid's algorithm

Highest Common Factor of 675,429,698 is 1

Step 1: Since 675 > 429, we apply the division lemma to 675 and 429, to get

675 = 429 x 1 + 246

Step 2: Since the reminder 429 ≠ 0, we apply division lemma to 246 and 429, to get

429 = 246 x 1 + 183

Step 3: We consider the new divisor 246 and the new remainder 183, and apply the division lemma to get

246 = 183 x 1 + 63

We consider the new divisor 183 and the new remainder 63,and apply the division lemma to get

183 = 63 x 2 + 57

We consider the new divisor 63 and the new remainder 57,and apply the division lemma to get

63 = 57 x 1 + 6

We consider the new divisor 57 and the new remainder 6,and apply the division lemma to get

57 = 6 x 9 + 3

We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get

6 = 3 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 675 and 429 is 3

Notice that 3 = HCF(6,3) = HCF(57,6) = HCF(63,57) = HCF(183,63) = HCF(246,183) = HCF(429,246) = HCF(675,429) .

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

Step 1: Since 698 > 3, we apply the division lemma to 698 and 3, to get

698 = 3 x 232 + 2

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

3 = 2 x 1 + 1

Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma 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 3 and 698 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(698,3) .

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Frequently Asked Questions on HCF of 675, 429, 698 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 675, 429, 698?

Answer: HCF of 675, 429, 698 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 675, 429, 698 using Euclid's Algorithm?

Answer: For arbitrary numbers 675, 429, 698 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.