Highest Common Factor of 4054, 4998, 61065 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 4054, 4998, 61065 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 4054, 4998, 61065 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 4054, 4998, 61065 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 4054, 4998, 61065 is 1.
HCF(4054, 4998, 61065) = 1
HCF of 4054, 4998, 61065 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 4054, 4998, 61065 is 1.
Highest Common Factor of 4054,4998,61065 is 1
Step 1: Since 4998 > 4054, we apply the division lemma to 4998 and 4054, to get
4998 = 4054 x 1 + 944
Step 2: Since the reminder 4054 ≠ 0, we apply division lemma to 944 and 4054, to get
4054 = 944 x 4 + 278
Step 3: We consider the new divisor 944 and the new remainder 278, and apply the division lemma to get
944 = 278 x 3 + 110
We consider the new divisor 278 and the new remainder 110,and apply the division lemma to get
278 = 110 x 2 + 58
We consider the new divisor 110 and the new remainder 58,and apply the division lemma to get
110 = 58 x 1 + 52
We consider the new divisor 58 and the new remainder 52,and apply the division lemma to get
58 = 52 x 1 + 6
We consider the new divisor 52 and the new remainder 6,and apply the division lemma to get
52 = 6 x 8 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 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 4054 and 4998 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(52,6) = HCF(58,52) = HCF(110,58) = HCF(278,110) = HCF(944,278) = HCF(4054,944) = HCF(4998,4054) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 61065 > 2, we apply the division lemma to 61065 and 2, to get
61065 = 2 x 30532 + 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 61065 is 1
Notice that 1 = HCF(2,1) = HCF(61065,2) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 4054, 4998, 61065 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 4054, 4998, 61065?
Answer: HCF of 4054, 4998, 61065 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 4054, 4998, 61065 using Euclid's Algorithm?
Answer: For arbitrary numbers 4054, 4998, 61065 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
