Highest Common Factor of 5946, 8420 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 5946, 8420 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 5946, 8420 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 5946, 8420 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 5946, 8420 is 2.
HCF(5946, 8420) = 2
HCF of 5946, 8420 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 5946, 8420 is 2.
Highest Common Factor of 5946,8420 is 2
Step 1: Since 8420 > 5946, we apply the division lemma to 8420 and 5946, to get
8420 = 5946 x 1 + 2474
Step 2: Since the reminder 5946 ≠ 0, we apply division lemma to 2474 and 5946, to get
5946 = 2474 x 2 + 998
Step 3: We consider the new divisor 2474 and the new remainder 998, and apply the division lemma to get
2474 = 998 x 2 + 478
We consider the new divisor 998 and the new remainder 478,and apply the division lemma to get
998 = 478 x 2 + 42
We consider the new divisor 478 and the new remainder 42,and apply the division lemma to get
478 = 42 x 11 + 16
We consider the new divisor 42 and the new remainder 16,and apply the division lemma to get
42 = 16 x 2 + 10
We consider the new divisor 16 and the new remainder 10,and apply the division lemma to get
16 = 10 x 1 + 6
We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get
10 = 6 x 1 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 5946 and 8420 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(16,10) = HCF(42,16) = HCF(478,42) = HCF(998,478) = HCF(2474,998) = HCF(5946,2474) = HCF(8420,5946) .
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Frequently Asked Questions on HCF of 5946, 8420 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 5946, 8420?
Answer: HCF of 5946, 8420 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 5946, 8420 using Euclid's Algorithm?
Answer: For arbitrary numbers 5946, 8420 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
