Highest Common Factor of 544, 854, 106 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 544, 854, 106 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 544, 854, 106 is 2 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 544, 854, 106 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 544, 854, 106 is 2.
HCF(544, 854, 106) = 2
HCF of 544, 854, 106 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 544, 854, 106 is 2.
Highest Common Factor of 544,854,106 is 2
Step 1: Since 854 > 544, we apply the division lemma to 854 and 544, to get
854 = 544 x 1 + 310
Step 2: Since the reminder 544 ≠ 0, we apply division lemma to 310 and 544, to get
544 = 310 x 1 + 234
Step 3: We consider the new divisor 310 and the new remainder 234, and apply the division lemma to get
310 = 234 x 1 + 76
We consider the new divisor 234 and the new remainder 76,and apply the division lemma to get
234 = 76 x 3 + 6
We consider the new divisor 76 and the new remainder 6,and apply the division lemma to get
76 = 6 x 12 + 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 544 and 854 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(76,6) = HCF(234,76) = HCF(310,234) = HCF(544,310) = HCF(854,544) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 106 > 2, we apply the division lemma to 106 and 2, to get
106 = 2 x 53 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 106 is 2
Notice that 2 = HCF(106,2) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 544, 854, 106 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 544, 854, 106?
Answer: HCF of 544, 854, 106 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 544, 854, 106 using Euclid's Algorithm?
Answer: For arbitrary numbers 544, 854, 106 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.