Highest Common Factor of 416, 651, 764 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 416, 651, 764 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 416, 651, 764 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 416, 651, 764 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 416, 651, 764 is 1.

HCF(416, 651, 764) = 1

HCF of 416, 651, 764 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 416, 651, 764 is 1.

Highest Common Factor of 416,651,764 using Euclid's algorithm

Highest Common Factor of 416,651,764 is 1

Step 1: Since 651 > 416, we apply the division lemma to 651 and 416, to get

651 = 416 x 1 + 235

Step 2: Since the reminder 416 ≠ 0, we apply division lemma to 235 and 416, to get

416 = 235 x 1 + 181

Step 3: We consider the new divisor 235 and the new remainder 181, and apply the division lemma to get

235 = 181 x 1 + 54

We consider the new divisor 181 and the new remainder 54,and apply the division lemma to get

181 = 54 x 3 + 19

We consider the new divisor 54 and the new remainder 19,and apply the division lemma to get

54 = 19 x 2 + 16

We consider the new divisor 19 and the new remainder 16,and apply the division lemma to get

19 = 16 x 1 + 3

We consider the new divisor 16 and the new remainder 3,and apply the division lemma to get

16 = 3 x 5 + 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 416 and 651 is 1

Notice that 1 = HCF(3,1) = HCF(16,3) = HCF(19,16) = HCF(54,19) = HCF(181,54) = HCF(235,181) = HCF(416,235) = HCF(651,416) .

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

Step 1: Since 764 > 1, we apply the division lemma to 764 and 1, to get

764 = 1 x 764 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 764 is 1

Notice that 1 = HCF(764,1) .

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Frequently Asked Questions on HCF of 416, 651, 764 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 416, 651, 764?

Answer: HCF of 416, 651, 764 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 416, 651, 764 using Euclid's Algorithm?

Answer: For arbitrary numbers 416, 651, 764 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.