Highest Common Factor of 3688, 3188, 69574 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 3688, 3188, 69574 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 3688, 3188, 69574 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 3688, 3188, 69574 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 3688, 3188, 69574 is 2.
HCF(3688, 3188, 69574) = 2
HCF of 3688, 3188, 69574 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 3688, 3188, 69574 is 2.
Highest Common Factor of 3688,3188,69574 is 2
Step 1: Since 3688 > 3188, we apply the division lemma to 3688 and 3188, to get
3688 = 3188 x 1 + 500
Step 2: Since the reminder 3188 ≠ 0, we apply division lemma to 500 and 3188, to get
3188 = 500 x 6 + 188
Step 3: We consider the new divisor 500 and the new remainder 188, and apply the division lemma to get
500 = 188 x 2 + 124
We consider the new divisor 188 and the new remainder 124,and apply the division lemma to get
188 = 124 x 1 + 64
We consider the new divisor 124 and the new remainder 64,and apply the division lemma to get
124 = 64 x 1 + 60
We consider the new divisor 64 and the new remainder 60,and apply the division lemma to get
64 = 60 x 1 + 4
We consider the new divisor 60 and the new remainder 4,and apply the division lemma to get
60 = 4 x 15 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 3688 and 3188 is 4
Notice that 4 = HCF(60,4) = HCF(64,60) = HCF(124,64) = HCF(188,124) = HCF(500,188) = HCF(3188,500) = HCF(3688,3188) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 69574 > 4, we apply the division lemma to 69574 and 4, to get
69574 = 4 x 17393 + 2
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, 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 4 and 69574 is 2
Notice that 2 = HCF(4,2) = HCF(69574,4) .
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Frequently Asked Questions on HCF of 3688, 3188, 69574 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 3688, 3188, 69574?
Answer: HCF of 3688, 3188, 69574 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 3688, 3188, 69574 using Euclid's Algorithm?
Answer: For arbitrary numbers 3688, 3188, 69574 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.