Highest Common Factor of 5364, 6998 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 5364, 6998 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 5364, 6998 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 5364, 6998 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 5364, 6998 is 2.
HCF(5364, 6998) = 2
HCF of 5364, 6998 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 5364, 6998 is 2.
Highest Common Factor of 5364,6998 is 2
Step 1: Since 6998 > 5364, we apply the division lemma to 6998 and 5364, to get
6998 = 5364 x 1 + 1634
Step 2: Since the reminder 5364 ≠ 0, we apply division lemma to 1634 and 5364, to get
5364 = 1634 x 3 + 462
Step 3: We consider the new divisor 1634 and the new remainder 462, and apply the division lemma to get
1634 = 462 x 3 + 248
We consider the new divisor 462 and the new remainder 248,and apply the division lemma to get
462 = 248 x 1 + 214
We consider the new divisor 248 and the new remainder 214,and apply the division lemma to get
248 = 214 x 1 + 34
We consider the new divisor 214 and the new remainder 34,and apply the division lemma to get
214 = 34 x 6 + 10
We consider the new divisor 34 and the new remainder 10,and apply the division lemma to get
34 = 10 x 3 + 4
We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get
10 = 4 x 2 + 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 5364 and 6998 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(34,10) = HCF(214,34) = HCF(248,214) = HCF(462,248) = HCF(1634,462) = HCF(5364,1634) = HCF(6998,5364) .
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Frequently Asked Questions on HCF of 5364, 6998 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 5364, 6998?
Answer: HCF of 5364, 6998 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 5364, 6998 using Euclid's Algorithm?
Answer: For arbitrary numbers 5364, 6998 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.