Highest Common Factor of 781, 332, 132 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 781, 332, 132 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 781, 332, 132 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 781, 332, 132 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 781, 332, 132 is 1.

HCF(781, 332, 132) = 1

HCF of 781, 332, 132 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 781, 332, 132 is 1.

Highest Common Factor of 781,332,132 using Euclid's algorithm

Highest Common Factor of 781,332,132 is 1

Step 1: Since 781 > 332, we apply the division lemma to 781 and 332, to get

781 = 332 x 2 + 117

Step 2: Since the reminder 332 ≠ 0, we apply division lemma to 117 and 332, to get

332 = 117 x 2 + 98

Step 3: We consider the new divisor 117 and the new remainder 98, and apply the division lemma to get

117 = 98 x 1 + 19

We consider the new divisor 98 and the new remainder 19,and apply the division lemma to get

98 = 19 x 5 + 3

We consider the new divisor 19 and the new remainder 3,and apply the division lemma to get

19 = 3 x 6 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 781 and 332 is 1

Notice that 1 = HCF(3,1) = HCF(19,3) = HCF(98,19) = HCF(117,98) = HCF(332,117) = HCF(781,332) .

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

Step 1: Since 132 > 1, we apply the division lemma to 132 and 1, to get

132 = 1 x 132 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 132 is 1

Notice that 1 = HCF(132,1) .

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Frequently Asked Questions on HCF of 781, 332, 132 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 781, 332, 132?

Answer: HCF of 781, 332, 132 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 781, 332, 132 using Euclid's Algorithm?

Answer: For arbitrary numbers 781, 332, 132 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.