Highest Common Factor of 429, 7035, 6458 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 429, 7035, 6458 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 429, 7035, 6458 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 429, 7035, 6458 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 429, 7035, 6458 is 1.

HCF(429, 7035, 6458) = 1

HCF of 429, 7035, 6458 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 429, 7035, 6458 is 1.

Highest Common Factor of 429,7035,6458 using Euclid's algorithm

Highest Common Factor of 429,7035,6458 is 1

Step 1: Since 7035 > 429, we apply the division lemma to 7035 and 429, to get

7035 = 429 x 16 + 171

Step 2: Since the reminder 429 ≠ 0, we apply division lemma to 171 and 429, to get

429 = 171 x 2 + 87

Step 3: We consider the new divisor 171 and the new remainder 87, and apply the division lemma to get

171 = 87 x 1 + 84

We consider the new divisor 87 and the new remainder 84,and apply the division lemma to get

87 = 84 x 1 + 3

We consider the new divisor 84 and the new remainder 3,and apply the division lemma to get

84 = 3 x 28 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 429 and 7035 is 3

Notice that 3 = HCF(84,3) = HCF(87,84) = HCF(171,87) = HCF(429,171) = HCF(7035,429) .

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

Step 1: Since 6458 > 3, we apply the division lemma to 6458 and 3, to get

6458 = 3 x 2152 + 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 6458 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(6458,3) .

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Frequently Asked Questions on HCF of 429, 7035, 6458 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 429, 7035, 6458?

Answer: HCF of 429, 7035, 6458 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 429, 7035, 6458 using Euclid's Algorithm?

Answer: For arbitrary numbers 429, 7035, 6458 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.