Highest Common Factor of 2098, 7768 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 2098, 7768 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 2098, 7768 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 2098, 7768 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 2098, 7768 is 2.
HCF(2098, 7768) = 2
HCF of 2098, 7768 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2098, 7768 is 2.
Highest Common Factor of 2098,7768 is 2
Step 1: Since 7768 > 2098, we apply the division lemma to 7768 and 2098, to get
7768 = 2098 x 3 + 1474
Step 2: Since the reminder 2098 ≠ 0, we apply division lemma to 1474 and 2098, to get
2098 = 1474 x 1 + 624
Step 3: We consider the new divisor 1474 and the new remainder 624, and apply the division lemma to get
1474 = 624 x 2 + 226
We consider the new divisor 624 and the new remainder 226,and apply the division lemma to get
624 = 226 x 2 + 172
We consider the new divisor 226 and the new remainder 172,and apply the division lemma to get
226 = 172 x 1 + 54
We consider the new divisor 172 and the new remainder 54,and apply the division lemma to get
172 = 54 x 3 + 10
We consider the new divisor 54 and the new remainder 10,and apply the division lemma to get
54 = 10 x 5 + 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 2098 and 7768 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(54,10) = HCF(172,54) = HCF(226,172) = HCF(624,226) = HCF(1474,624) = HCF(2098,1474) = HCF(7768,2098) .
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Frequently Asked Questions on HCF of 2098, 7768 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 2098, 7768?
Answer: HCF of 2098, 7768 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2098, 7768 using Euclid's Algorithm?
Answer: For arbitrary numbers 2098, 7768 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.