Highest Common Factor of 3702, 2708 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 3702, 2708 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 3702, 2708 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 3702, 2708 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 3702, 2708 is 2.
HCF(3702, 2708) = 2
HCF of 3702, 2708 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 3702, 2708 is 2.
Highest Common Factor of 3702,2708 is 2
Step 1: Since 3702 > 2708, we apply the division lemma to 3702 and 2708, to get
3702 = 2708 x 1 + 994
Step 2: Since the reminder 2708 ≠ 0, we apply division lemma to 994 and 2708, to get
2708 = 994 x 2 + 720
Step 3: We consider the new divisor 994 and the new remainder 720, and apply the division lemma to get
994 = 720 x 1 + 274
We consider the new divisor 720 and the new remainder 274,and apply the division lemma to get
720 = 274 x 2 + 172
We consider the new divisor 274 and the new remainder 172,and apply the division lemma to get
274 = 172 x 1 + 102
We consider the new divisor 172 and the new remainder 102,and apply the division lemma to get
172 = 102 x 1 + 70
We consider the new divisor 102 and the new remainder 70,and apply the division lemma to get
102 = 70 x 1 + 32
We consider the new divisor 70 and the new remainder 32,and apply the division lemma to get
70 = 32 x 2 + 6
We consider the new divisor 32 and the new remainder 6,and apply the division lemma to get
32 = 6 x 5 + 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 3702 and 2708 is 2
Notice that 2 = HCF(6,2) = HCF(32,6) = HCF(70,32) = HCF(102,70) = HCF(172,102) = HCF(274,172) = HCF(720,274) = HCF(994,720) = HCF(2708,994) = HCF(3702,2708) .
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Frequently Asked Questions on HCF of 3702, 2708 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 3702, 2708?
Answer: HCF of 3702, 2708 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 3702, 2708 using Euclid's Algorithm?
Answer: For arbitrary numbers 3702, 2708 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.