Highest Common Factor of 7098, 7708 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 7098, 7708 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 7098, 7708 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 7098, 7708 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 7098, 7708 is 2.
HCF(7098, 7708) = 2
HCF of 7098, 7708 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7098, 7708 is 2.
Highest Common Factor of 7098,7708 is 2
Step 1: Since 7708 > 7098, we apply the division lemma to 7708 and 7098, to get
7708 = 7098 x 1 + 610
Step 2: Since the reminder 7098 ≠ 0, we apply division lemma to 610 and 7098, to get
7098 = 610 x 11 + 388
Step 3: We consider the new divisor 610 and the new remainder 388, and apply the division lemma to get
610 = 388 x 1 + 222
We consider the new divisor 388 and the new remainder 222,and apply the division lemma to get
388 = 222 x 1 + 166
We consider the new divisor 222 and the new remainder 166,and apply the division lemma to get
222 = 166 x 1 + 56
We consider the new divisor 166 and the new remainder 56,and apply the division lemma to get
166 = 56 x 2 + 54
We consider the new divisor 56 and the new remainder 54,and apply the division lemma to get
56 = 54 x 1 + 2
We consider the new divisor 54 and the new remainder 2,and apply the division lemma to get
54 = 2 x 27 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 7098 and 7708 is 2
Notice that 2 = HCF(54,2) = HCF(56,54) = HCF(166,56) = HCF(222,166) = HCF(388,222) = HCF(610,388) = HCF(7098,610) = HCF(7708,7098) .
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Frequently Asked Questions on HCF of 7098, 7708 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 7098, 7708?
Answer: HCF of 7098, 7708 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7098, 7708 using Euclid's Algorithm?
Answer: For arbitrary numbers 7098, 7708 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.