Highest Common Factor of 982, 714, 232 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 982, 714, 232 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 982, 714, 232 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 982, 714, 232 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 982, 714, 232 is 2.

HCF(982, 714, 232) = 2

HCF of 982, 714, 232 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 982, 714, 232 is 2.

Highest Common Factor of 982,714,232 using Euclid's algorithm

Highest Common Factor of 982,714,232 is 2

Step 1: Since 982 > 714, we apply the division lemma to 982 and 714, to get

982 = 714 x 1 + 268

Step 2: Since the reminder 714 ≠ 0, we apply division lemma to 268 and 714, to get

714 = 268 x 2 + 178

Step 3: We consider the new divisor 268 and the new remainder 178, and apply the division lemma to get

268 = 178 x 1 + 90

We consider the new divisor 178 and the new remainder 90,and apply the division lemma to get

178 = 90 x 1 + 88

We consider the new divisor 90 and the new remainder 88,and apply the division lemma to get

90 = 88 x 1 + 2

We consider the new divisor 88 and the new remainder 2,and apply the division lemma to get

88 = 2 x 44 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 982 and 714 is 2

Notice that 2 = HCF(88,2) = HCF(90,88) = HCF(178,90) = HCF(268,178) = HCF(714,268) = HCF(982,714) .

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

Step 1: Since 232 > 2, we apply the division lemma to 232 and 2, to get

232 = 2 x 116 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 232 is 2

Notice that 2 = HCF(232,2) .

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Frequently Asked Questions on HCF of 982, 714, 232 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 982, 714, 232?

Answer: HCF of 982, 714, 232 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 982, 714, 232 using Euclid's Algorithm?

Answer: For arbitrary numbers 982, 714, 232 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.