Highest Common Factor of 830, 688, 283 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 830, 688, 283 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 830, 688, 283 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 830, 688, 283 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 830, 688, 283 is 1.

HCF(830, 688, 283) = 1

HCF of 830, 688, 283 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 830, 688, 283 is 1.

Highest Common Factor of 830,688,283 using Euclid's algorithm

Highest Common Factor of 830,688,283 is 1

Step 1: Since 830 > 688, we apply the division lemma to 830 and 688, to get

830 = 688 x 1 + 142

Step 2: Since the reminder 688 ≠ 0, we apply division lemma to 142 and 688, to get

688 = 142 x 4 + 120

Step 3: We consider the new divisor 142 and the new remainder 120, and apply the division lemma to get

142 = 120 x 1 + 22

We consider the new divisor 120 and the new remainder 22,and apply the division lemma to get

120 = 22 x 5 + 10

We consider the new divisor 22 and the new remainder 10,and apply the division lemma to get

22 = 10 x 2 + 2

We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get

10 = 2 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 830 and 688 is 2

Notice that 2 = HCF(10,2) = HCF(22,10) = HCF(120,22) = HCF(142,120) = HCF(688,142) = HCF(830,688) .

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

Step 1: Since 283 > 2, we apply the division lemma to 283 and 2, to get

283 = 2 x 141 + 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 283 is 1

Notice that 1 = HCF(2,1) = HCF(283,2) .

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Frequently Asked Questions on HCF of 830, 688, 283 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 830, 688, 283?

Answer: HCF of 830, 688, 283 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 830, 688, 283 using Euclid's Algorithm?

Answer: For arbitrary numbers 830, 688, 283 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.