Highest Common Factor of 774, 701, 520 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 774, 701, 520 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 774, 701, 520 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 774, 701, 520 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 774, 701, 520 is 1.

HCF(774, 701, 520) = 1

HCF of 774, 701, 520 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 774, 701, 520 is 1.

Highest Common Factor of 774,701,520 using Euclid's algorithm

Highest Common Factor of 774,701,520 is 1

Step 1: Since 774 > 701, we apply the division lemma to 774 and 701, to get

774 = 701 x 1 + 73

Step 2: Since the reminder 701 ≠ 0, we apply division lemma to 73 and 701, to get

701 = 73 x 9 + 44

Step 3: We consider the new divisor 73 and the new remainder 44, and apply the division lemma to get

73 = 44 x 1 + 29

We consider the new divisor 44 and the new remainder 29,and apply the division lemma to get

44 = 29 x 1 + 15

We consider the new divisor 29 and the new remainder 15,and apply the division lemma to get

29 = 15 x 1 + 14

We consider the new divisor 15 and the new remainder 14,and apply the division lemma to get

15 = 14 x 1 + 1

We consider the new divisor 14 and the new remainder 1,and apply the division lemma to get

14 = 1 x 14 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 774 and 701 is 1

Notice that 1 = HCF(14,1) = HCF(15,14) = HCF(29,15) = HCF(44,29) = HCF(73,44) = HCF(701,73) = HCF(774,701) .

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

Step 1: Since 520 > 1, we apply the division lemma to 520 and 1, to get

520 = 1 x 520 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 520 is 1

Notice that 1 = HCF(520,1) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 774, 701, 520 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 774, 701, 520?

Answer: HCF of 774, 701, 520 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 774, 701, 520 using Euclid's Algorithm?

Answer: For arbitrary numbers 774, 701, 520 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.