Highest Common Factor of 107, 54909 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 107, 54909 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 107, 54909 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 107, 54909 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 107, 54909 is 1.
HCF(107, 54909) = 1
HCF of 107, 54909 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 107, 54909 is 1.
Highest Common Factor of 107,54909 is 1
Step 1: Since 54909 > 107, we apply the division lemma to 54909 and 107, to get
54909 = 107 x 513 + 18
Step 2: Since the reminder 107 ≠ 0, we apply division lemma to 18 and 107, to get
107 = 18 x 5 + 17
Step 3: We consider the new divisor 18 and the new remainder 17, and apply the division lemma to get
18 = 17 x 1 + 1
We consider the new divisor 17 and the new remainder 1, and apply the division lemma to get
17 = 1 x 17 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 107 and 54909 is 1
Notice that 1 = HCF(17,1) = HCF(18,17) = HCF(107,18) = HCF(54909,107) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 107, 54909 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 107, 54909?
Answer: HCF of 107, 54909 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 107, 54909 using Euclid's Algorithm?
Answer: For arbitrary numbers 107, 54909 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.