Highest Common Factor of 4138, 5305 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 4138, 5305 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 4138, 5305 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 4138, 5305 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 4138, 5305 is 1.
HCF(4138, 5305) = 1
HCF of 4138, 5305 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 4138, 5305 is 1.
Highest Common Factor of 4138,5305 is 1
Step 1: Since 5305 > 4138, we apply the division lemma to 5305 and 4138, to get
5305 = 4138 x 1 + 1167
Step 2: Since the reminder 4138 ≠ 0, we apply division lemma to 1167 and 4138, to get
4138 = 1167 x 3 + 637
Step 3: We consider the new divisor 1167 and the new remainder 637, and apply the division lemma to get
1167 = 637 x 1 + 530
We consider the new divisor 637 and the new remainder 530,and apply the division lemma to get
637 = 530 x 1 + 107
We consider the new divisor 530 and the new remainder 107,and apply the division lemma to get
530 = 107 x 4 + 102
We consider the new divisor 107 and the new remainder 102,and apply the division lemma to get
107 = 102 x 1 + 5
We consider the new divisor 102 and the new remainder 5,and apply the division lemma to get
102 = 5 x 20 + 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 4138 and 5305 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(102,5) = HCF(107,102) = HCF(530,107) = HCF(637,530) = HCF(1167,637) = HCF(4138,1167) = HCF(5305,4138) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 4138, 5305 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 4138, 5305?
Answer: HCF of 4138, 5305 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 4138, 5305 using Euclid's Algorithm?
Answer: For arbitrary numbers 4138, 5305 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.