Highest Common Factor of 305, 868, 709 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 305, 868, 709 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 305, 868, 709 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 305, 868, 709 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 305, 868, 709 is 1.
HCF(305, 868, 709) = 1
HCF of 305, 868, 709 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 305, 868, 709 is 1.
Highest Common Factor of 305,868,709 is 1
Step 1: Since 868 > 305, we apply the division lemma to 868 and 305, to get
868 = 305 x 2 + 258
Step 2: Since the reminder 305 ≠ 0, we apply division lemma to 258 and 305, to get
305 = 258 x 1 + 47
Step 3: We consider the new divisor 258 and the new remainder 47, and apply the division lemma to get
258 = 47 x 5 + 23
We consider the new divisor 47 and the new remainder 23,and apply the division lemma to get
47 = 23 x 2 + 1
We consider the new divisor 23 and the new remainder 1,and apply the division lemma to get
23 = 1 x 23 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 305 and 868 is 1
Notice that 1 = HCF(23,1) = HCF(47,23) = HCF(258,47) = HCF(305,258) = HCF(868,305) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 709 > 1, we apply the division lemma to 709 and 1, to get
709 = 1 x 709 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 709 is 1
Notice that 1 = HCF(709,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 305, 868, 709 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 305, 868, 709?
Answer: HCF of 305, 868, 709 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 305, 868, 709 using Euclid's Algorithm?
Answer: For arbitrary numbers 305, 868, 709 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.