Highest Common Factor of 5854, 8538 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 5854, 8538 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 5854, 8538 is 2 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 5854, 8538 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 5854, 8538 is 2.
HCF(5854, 8538) = 2
HCF of 5854, 8538 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 5854, 8538 is 2.
Highest Common Factor of 5854,8538 is 2
Step 1: Since 8538 > 5854, we apply the division lemma to 8538 and 5854, to get
8538 = 5854 x 1 + 2684
Step 2: Since the reminder 5854 ≠ 0, we apply division lemma to 2684 and 5854, to get
5854 = 2684 x 2 + 486
Step 3: We consider the new divisor 2684 and the new remainder 486, and apply the division lemma to get
2684 = 486 x 5 + 254
We consider the new divisor 486 and the new remainder 254,and apply the division lemma to get
486 = 254 x 1 + 232
We consider the new divisor 254 and the new remainder 232,and apply the division lemma to get
254 = 232 x 1 + 22
We consider the new divisor 232 and the new remainder 22,and apply the division lemma to get
232 = 22 x 10 + 12
We consider the new divisor 22 and the new remainder 12,and apply the division lemma to get
22 = 12 x 1 + 10
We consider the new divisor 12 and the new remainder 10,and apply the division lemma to get
12 = 10 x 1 + 2
We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 5854 and 8538 is 2
Notice that 2 = HCF(10,2) = HCF(12,10) = HCF(22,12) = HCF(232,22) = HCF(254,232) = HCF(486,254) = HCF(2684,486) = HCF(5854,2684) = HCF(8538,5854) .
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Frequently Asked Questions on HCF of 5854, 8538 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 5854, 8538?
Answer: HCF of 5854, 8538 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 5854, 8538 using Euclid's Algorithm?
Answer: For arbitrary numbers 5854, 8538 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.