Highest Common Factor of 782, 988, 910 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 782, 988, 910 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 782, 988, 910 is 2 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 782, 988, 910 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 782, 988, 910 is 2.

HCF(782, 988, 910) = 2

HCF of 782, 988, 910 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 782, 988, 910 is 2.

Highest Common Factor of 782,988,910 using Euclid's algorithm

Highest Common Factor of 782,988,910 is 2

Step 1: Since 988 > 782, we apply the division lemma to 988 and 782, to get

988 = 782 x 1 + 206

Step 2: Since the reminder 782 ≠ 0, we apply division lemma to 206 and 782, to get

782 = 206 x 3 + 164

Step 3: We consider the new divisor 206 and the new remainder 164, and apply the division lemma to get

206 = 164 x 1 + 42

We consider the new divisor 164 and the new remainder 42,and apply the division lemma to get

164 = 42 x 3 + 38

We consider the new divisor 42 and the new remainder 38,and apply the division lemma to get

42 = 38 x 1 + 4

We consider the new divisor 38 and the new remainder 4,and apply the division lemma to get

38 = 4 x 9 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 782 and 988 is 2

Notice that 2 = HCF(4,2) = HCF(38,4) = HCF(42,38) = HCF(164,42) = HCF(206,164) = HCF(782,206) = HCF(988,782) .

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

Step 1: Since 910 > 2, we apply the division lemma to 910 and 2, to get

910 = 2 x 455 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 910 is 2

Notice that 2 = HCF(910,2) .

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Frequently Asked Questions on HCF of 782, 988, 910 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 782, 988, 910?

Answer: HCF of 782, 988, 910 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 782, 988, 910 using Euclid's Algorithm?

Answer: For arbitrary numbers 782, 988, 910 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.