Highest Common Factor of 688, 65 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 688, 65 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 688, 65 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 688, 65 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 688, 65 is 1.
HCF(688, 65) = 1
HCF of 688, 65 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 688, 65 is 1.
Highest Common Factor of 688,65 is 1
Step 1: Since 688 > 65, we apply the division lemma to 688 and 65, to get
688 = 65 x 10 + 38
Step 2: Since the reminder 65 ≠ 0, we apply division lemma to 38 and 65, to get
65 = 38 x 1 + 27
Step 3: We consider the new divisor 38 and the new remainder 27, and apply the division lemma to get
38 = 27 x 1 + 11
We consider the new divisor 27 and the new remainder 11,and apply the division lemma to get
27 = 11 x 2 + 5
We consider the new divisor 11 and the new remainder 5,and apply the division lemma to get
11 = 5 x 2 + 1
We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 688 and 65 is 1
Notice that 1 = HCF(5,1) = HCF(11,5) = HCF(27,11) = HCF(38,27) = HCF(65,38) = HCF(688,65) .
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Frequently Asked Questions on HCF of 688, 65 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 688, 65?
Answer: HCF of 688, 65 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 688, 65 using Euclid's Algorithm?
Answer: For arbitrary numbers 688, 65 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.