Highest Common Factor of 5774, 6720, 44561 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 5774, 6720, 44561 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 5774, 6720, 44561 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 5774, 6720, 44561 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 5774, 6720, 44561 is 1.

HCF(5774, 6720, 44561) = 1

HCF of 5774, 6720, 44561 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 5774, 6720, 44561 is 1.

Highest Common Factor of 5774,6720,44561 using Euclid's algorithm

Highest Common Factor of 5774,6720,44561 is 1

Step 1: Since 6720 > 5774, we apply the division lemma to 6720 and 5774, to get

6720 = 5774 x 1 + 946

Step 2: Since the reminder 5774 ≠ 0, we apply division lemma to 946 and 5774, to get

5774 = 946 x 6 + 98

Step 3: We consider the new divisor 946 and the new remainder 98, and apply the division lemma to get

946 = 98 x 9 + 64

We consider the new divisor 98 and the new remainder 64,and apply the division lemma to get

98 = 64 x 1 + 34

We consider the new divisor 64 and the new remainder 34,and apply the division lemma to get

64 = 34 x 1 + 30

We consider the new divisor 34 and the new remainder 30,and apply the division lemma to get

34 = 30 x 1 + 4

We consider the new divisor 30 and the new remainder 4,and apply the division lemma to get

30 = 4 x 7 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 5774 and 6720 is 2

Notice that 2 = HCF(4,2) = HCF(30,4) = HCF(34,30) = HCF(64,34) = HCF(98,64) = HCF(946,98) = HCF(5774,946) = HCF(6720,5774) .

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

Step 1: Since 44561 > 2, we apply the division lemma to 44561 and 2, to get

44561 = 2 x 22280 + 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 44561 is 1

Notice that 1 = HCF(2,1) = HCF(44561,2) .

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Frequently Asked Questions on HCF of 5774, 6720, 44561 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 5774, 6720, 44561?

Answer: HCF of 5774, 6720, 44561 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 5774, 6720, 44561 using Euclid's Algorithm?

Answer: For arbitrary numbers 5774, 6720, 44561 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.