Highest Common Factor of 710, 429, 816 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 710, 429, 816 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 710, 429, 816 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 710, 429, 816 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 710, 429, 816 is 1.

HCF(710, 429, 816) = 1

HCF of 710, 429, 816 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 710, 429, 816 is 1.

Highest Common Factor of 710,429,816 using Euclid's algorithm

Highest Common Factor of 710,429,816 is 1

Step 1: Since 710 > 429, we apply the division lemma to 710 and 429, to get

710 = 429 x 1 + 281

Step 2: Since the reminder 429 ≠ 0, we apply division lemma to 281 and 429, to get

429 = 281 x 1 + 148

Step 3: We consider the new divisor 281 and the new remainder 148, and apply the division lemma to get

281 = 148 x 1 + 133

We consider the new divisor 148 and the new remainder 133,and apply the division lemma to get

148 = 133 x 1 + 15

We consider the new divisor 133 and the new remainder 15,and apply the division lemma to get

133 = 15 x 8 + 13

We consider the new divisor 15 and the new remainder 13,and apply the division lemma to get

15 = 13 x 1 + 2

We consider the new divisor 13 and the new remainder 2,and apply the division lemma to get

13 = 2 x 6 + 1

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 710 and 429 is 1

Notice that 1 = HCF(2,1) = HCF(13,2) = HCF(15,13) = HCF(133,15) = HCF(148,133) = HCF(281,148) = HCF(429,281) = HCF(710,429) .

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

Step 1: Since 816 > 1, we apply the division lemma to 816 and 1, to get

816 = 1 x 816 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 816 is 1

Notice that 1 = HCF(816,1) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 710, 429, 816 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 710, 429, 816?

Answer: HCF of 710, 429, 816 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 710, 429, 816 using Euclid's Algorithm?

Answer: For arbitrary numbers 710, 429, 816 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.