Highest Common Factor of 7984, 6698 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 7984, 6698 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 7984, 6698 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 7984, 6698 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 7984, 6698 is 2.
HCF(7984, 6698) = 2
HCF of 7984, 6698 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7984, 6698 is 2.
Highest Common Factor of 7984,6698 is 2
Step 1: Since 7984 > 6698, we apply the division lemma to 7984 and 6698, to get
7984 = 6698 x 1 + 1286
Step 2: Since the reminder 6698 ≠ 0, we apply division lemma to 1286 and 6698, to get
6698 = 1286 x 5 + 268
Step 3: We consider the new divisor 1286 and the new remainder 268, and apply the division lemma to get
1286 = 268 x 4 + 214
We consider the new divisor 268 and the new remainder 214,and apply the division lemma to get
268 = 214 x 1 + 54
We consider the new divisor 214 and the new remainder 54,and apply the division lemma to get
214 = 54 x 3 + 52
We consider the new divisor 54 and the new remainder 52,and apply the division lemma to get
54 = 52 x 1 + 2
We consider the new divisor 52 and the new remainder 2,and apply the division lemma to get
52 = 2 x 26 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 7984 and 6698 is 2
Notice that 2 = HCF(52,2) = HCF(54,52) = HCF(214,54) = HCF(268,214) = HCF(1286,268) = HCF(6698,1286) = HCF(7984,6698) .
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Frequently Asked Questions on HCF of 7984, 6698 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 7984, 6698?
Answer: HCF of 7984, 6698 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7984, 6698 using Euclid's Algorithm?
Answer: For arbitrary numbers 7984, 6698 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
