Highest Common Factor of 309, 898 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 309, 898 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 309, 898 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 309, 898 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 309, 898 is 1.
HCF(309, 898) = 1
HCF of 309, 898 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 309, 898 is 1.
Highest Common Factor of 309,898 is 1
Step 1: Since 898 > 309, we apply the division lemma to 898 and 309, to get
898 = 309 x 2 + 280
Step 2: Since the reminder 309 ≠ 0, we apply division lemma to 280 and 309, to get
309 = 280 x 1 + 29
Step 3: We consider the new divisor 280 and the new remainder 29, and apply the division lemma to get
280 = 29 x 9 + 19
We consider the new divisor 29 and the new remainder 19,and apply the division lemma to get
29 = 19 x 1 + 10
We consider the new divisor 19 and the new remainder 10,and apply the division lemma to get
19 = 10 x 1 + 9
We consider the new divisor 10 and the new remainder 9,and apply the division lemma to get
10 = 9 x 1 + 1
We consider the new divisor 9 and the new remainder 1,and apply the division lemma to get
9 = 1 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 309 and 898 is 1
Notice that 1 = HCF(9,1) = HCF(10,9) = HCF(19,10) = HCF(29,19) = HCF(280,29) = HCF(309,280) = HCF(898,309) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 309, 898 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 309, 898?
Answer: HCF of 309, 898 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 309, 898 using Euclid's Algorithm?
Answer: For arbitrary numbers 309, 898 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.