Highest Common Factor of 1696, 7378 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 1696, 7378 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 1696, 7378 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 1696, 7378 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 1696, 7378 is 2.
HCF(1696, 7378) = 2
HCF of 1696, 7378 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1696, 7378 is 2.
Highest Common Factor of 1696,7378 is 2
Step 1: Since 7378 > 1696, we apply the division lemma to 7378 and 1696, to get
7378 = 1696 x 4 + 594
Step 2: Since the reminder 1696 ≠ 0, we apply division lemma to 594 and 1696, to get
1696 = 594 x 2 + 508
Step 3: We consider the new divisor 594 and the new remainder 508, and apply the division lemma to get
594 = 508 x 1 + 86
We consider the new divisor 508 and the new remainder 86,and apply the division lemma to get
508 = 86 x 5 + 78
We consider the new divisor 86 and the new remainder 78,and apply the division lemma to get
86 = 78 x 1 + 8
We consider the new divisor 78 and the new remainder 8,and apply the division lemma to get
78 = 8 x 9 + 6
We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get
8 = 6 x 1 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 1696 and 7378 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(78,8) = HCF(86,78) = HCF(508,86) = HCF(594,508) = HCF(1696,594) = HCF(7378,1696) .
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Frequently Asked Questions on HCF of 1696, 7378 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 1696, 7378?
Answer: HCF of 1696, 7378 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1696, 7378 using Euclid's Algorithm?
Answer: For arbitrary numbers 1696, 7378 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.