Highest Common Factor of 65, 40, 688 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 65, 40, 688 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 65, 40, 688 is 1 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 65, 40, 688 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 65, 40, 688 is 1.
HCF(65, 40, 688) = 1
HCF of 65, 40, 688 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 65, 40, 688 is 1.
Highest Common Factor of 65,40,688 is 1
Step 1: Since 65 > 40, we apply the division lemma to 65 and 40, to get
65 = 40 x 1 + 25
Step 2: Since the reminder 40 ≠ 0, we apply division lemma to 25 and 40, to get
40 = 25 x 1 + 15
Step 3: We consider the new divisor 25 and the new remainder 15, and apply the division lemma to get
25 = 15 x 1 + 10
We consider the new divisor 15 and the new remainder 10,and apply the division lemma to get
15 = 10 x 1 + 5
We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get
10 = 5 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 65 and 40 is 5
Notice that 5 = HCF(10,5) = HCF(15,10) = HCF(25,15) = HCF(40,25) = HCF(65,40) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 688 > 5, we apply the division lemma to 688 and 5, to get
688 = 5 x 137 + 3
Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 3 and 5, to get
5 = 3 x 1 + 2
Step 3: We consider the new divisor 3 and the new remainder 2, and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5 and 688 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(688,5) .
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Frequently Asked Questions on HCF of 65, 40, 688 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 65, 40, 688?
Answer: HCF of 65, 40, 688 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 65, 40, 688 using Euclid's Algorithm?
Answer: For arbitrary numbers 65, 40, 688 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.