Highest Common Factor of 2123, 3707, 43242 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 2123, 3707, 43242 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 2123, 3707, 43242 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 2123, 3707, 43242 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 2123, 3707, 43242 is 1.
HCF(2123, 3707, 43242) = 1
HCF of 2123, 3707, 43242 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2123, 3707, 43242 is 1.
Highest Common Factor of 2123,3707,43242 is 1
Step 1: Since 3707 > 2123, we apply the division lemma to 3707 and 2123, to get
3707 = 2123 x 1 + 1584
Step 2: Since the reminder 2123 ≠ 0, we apply division lemma to 1584 and 2123, to get
2123 = 1584 x 1 + 539
Step 3: We consider the new divisor 1584 and the new remainder 539, and apply the division lemma to get
1584 = 539 x 2 + 506
We consider the new divisor 539 and the new remainder 506,and apply the division lemma to get
539 = 506 x 1 + 33
We consider the new divisor 506 and the new remainder 33,and apply the division lemma to get
506 = 33 x 15 + 11
We consider the new divisor 33 and the new remainder 11,and apply the division lemma to get
33 = 11 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 11, the HCF of 2123 and 3707 is 11
Notice that 11 = HCF(33,11) = HCF(506,33) = HCF(539,506) = HCF(1584,539) = HCF(2123,1584) = HCF(3707,2123) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 43242 > 11, we apply the division lemma to 43242 and 11, to get
43242 = 11 x 3931 + 1
Step 2: Since the reminder 11 ≠ 0, we apply division lemma to 1 and 11, to get
11 = 1 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 11 and 43242 is 1
Notice that 1 = HCF(11,1) = HCF(43242,11) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 2123, 3707, 43242 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 2123, 3707, 43242?
Answer: HCF of 2123, 3707, 43242 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2123, 3707, 43242 using Euclid's Algorithm?
Answer: For arbitrary numbers 2123, 3707, 43242 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.