Highest Common Factor of 854, 1037 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 854, 1037 i.e. 61 the largest integer that leaves a remainder zero for all numbers.
HCF of 854, 1037 is 61 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 854, 1037 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 854, 1037 is 61.
HCF(854, 1037) = 61
HCF of 854, 1037 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 854, 1037 is 61.
Highest Common Factor of 854,1037 is 61
Step 1: Since 1037 > 854, we apply the division lemma to 1037 and 854, to get
1037 = 854 x 1 + 183
Step 2: Since the reminder 854 ≠ 0, we apply division lemma to 183 and 854, to get
854 = 183 x 4 + 122
Step 3: We consider the new divisor 183 and the new remainder 122, and apply the division lemma to get
183 = 122 x 1 + 61
We consider the new divisor 122 and the new remainder 61, and apply the division lemma to get
122 = 61 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 61, the HCF of 854 and 1037 is 61
Notice that 61 = HCF(122,61) = HCF(183,122) = HCF(854,183) = HCF(1037,854) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 854, 1037 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 854, 1037?
Answer: HCF of 854, 1037 is 61 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 854, 1037 using Euclid's Algorithm?
Answer: For arbitrary numbers 854, 1037 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.