Highest Common Factor of 434, 746, 165, 777 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 434, 746, 165, 777 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 434, 746, 165, 777 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 434, 746, 165, 777 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 434, 746, 165, 777 is 1.

HCF(434, 746, 165, 777) = 1

HCF of 434, 746, 165, 777 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 434, 746, 165, 777 is 1.

Highest Common Factor of 434,746,165,777 using Euclid's algorithm

Highest Common Factor of 434,746,165,777 is 1

Step 1: Since 746 > 434, we apply the division lemma to 746 and 434, to get

746 = 434 x 1 + 312

Step 2: Since the reminder 434 ≠ 0, we apply division lemma to 312 and 434, to get

434 = 312 x 1 + 122

Step 3: We consider the new divisor 312 and the new remainder 122, and apply the division lemma to get

312 = 122 x 2 + 68

We consider the new divisor 122 and the new remainder 68,and apply the division lemma to get

122 = 68 x 1 + 54

We consider the new divisor 68 and the new remainder 54,and apply the division lemma to get

68 = 54 x 1 + 14

We consider the new divisor 54 and the new remainder 14,and apply the division lemma to get

54 = 14 x 3 + 12

We consider the new divisor 14 and the new remainder 12,and apply the division lemma to get

14 = 12 x 1 + 2

We consider the new divisor 12 and the new remainder 2,and apply the division lemma to get

12 = 2 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 434 and 746 is 2

Notice that 2 = HCF(12,2) = HCF(14,12) = HCF(54,14) = HCF(68,54) = HCF(122,68) = HCF(312,122) = HCF(434,312) = HCF(746,434) .

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

Step 1: Since 165 > 2, we apply the division lemma to 165 and 2, to get

165 = 2 x 82 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 165 is 1

Notice that 1 = HCF(2,1) = HCF(165,2) .

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

Step 1: Since 777 > 1, we apply the division lemma to 777 and 1, to get

777 = 1 x 777 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 777 is 1

Notice that 1 = HCF(777,1) .

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Frequently Asked Questions on HCF of 434, 746, 165, 777 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 434, 746, 165, 777?

Answer: HCF of 434, 746, 165, 777 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 434, 746, 165, 777 using Euclid's Algorithm?

Answer: For arbitrary numbers 434, 746, 165, 777 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.