Highest Common Factor of 46, 728, 184, 622 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 46, 728, 184, 622 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 46, 728, 184, 622 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 46, 728, 184, 622 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 46, 728, 184, 622 is 2.
HCF(46, 728, 184, 622) = 2
HCF of 46, 728, 184, 622 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 46, 728, 184, 622 is 2.
Highest Common Factor of 46,728,184,622 is 2
Step 1: Since 728 > 46, we apply the division lemma to 728 and 46, to get
728 = 46 x 15 + 38
Step 2: Since the reminder 46 ≠ 0, we apply division lemma to 38 and 46, to get
46 = 38 x 1 + 8
Step 3: We consider the new divisor 38 and the new remainder 8, and apply the division lemma to get
38 = 8 x 4 + 6
We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get
8 = 6 x 1 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 46 and 728 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(38,8) = HCF(46,38) = HCF(728,46) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 184 > 2, we apply the division lemma to 184 and 2, to get
184 = 2 x 92 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 184 is 2
Notice that 2 = HCF(184,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 622 > 2, we apply the division lemma to 622 and 2, to get
622 = 2 x 311 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 622 is 2
Notice that 2 = HCF(622,2) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 46, 728, 184, 622 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 46, 728, 184, 622?
Answer: HCF of 46, 728, 184, 622 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 46, 728, 184, 622 using Euclid's Algorithm?
Answer: For arbitrary numbers 46, 728, 184, 622 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.