Highest Common Factor of 408, 629, 46, 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 408, 629, 46, 106 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 408, 629, 46, 106 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 408, 629, 46, 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 408, 629, 46, 106 is 1.
HCF(408, 629, 46, 106) = 1
HCF of 408, 629, 46, 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 408, 629, 46, 106 is 1.
Highest Common Factor of 408,629,46,106 is 1
Step 1: Since 629 > 408, we apply the division lemma to 629 and 408, to get
629 = 408 x 1 + 221
Step 2: Since the reminder 408 ≠ 0, we apply division lemma to 221 and 408, to get
408 = 221 x 1 + 187
Step 3: We consider the new divisor 221 and the new remainder 187, and apply the division lemma to get
221 = 187 x 1 + 34
We consider the new divisor 187 and the new remainder 34,and apply the division lemma to get
187 = 34 x 5 + 17
We consider the new divisor 34 and the new remainder 17,and apply the division lemma to get
34 = 17 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 17, the HCF of 408 and 629 is 17
Notice that 17 = HCF(34,17) = HCF(187,34) = HCF(221,187) = HCF(408,221) = HCF(629,408) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 46 > 17, we apply the division lemma to 46 and 17, to get
46 = 17 x 2 + 12
Step 2: Since the reminder 17 ≠ 0, we apply division lemma to 12 and 17, to get
17 = 12 x 1 + 5
Step 3: We consider the new divisor 12 and the new remainder 5, and apply the division lemma to get
12 = 5 x 2 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 17 and 46 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(12,5) = HCF(17,12) = HCF(46,17) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 106 > 1, we apply the division lemma to 106 and 1, to get
106 = 1 x 106 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 106 is 1
Notice that 1 = HCF(106,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 408, 629, 46, 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 408, 629, 46, 106?
Answer: HCF of 408, 629, 46, 106 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 408, 629, 46, 106 using Euclid's Algorithm?
Answer: For arbitrary numbers 408, 629, 46, 106 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.