Highest Common Factor of 688, 365 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, 365 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 688, 365 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, 365 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, 365 is 1.
HCF(688, 365) = 1
HCF of 688, 365 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, 365 is 1.
Highest Common Factor of 688,365 is 1
Step 1: Since 688 > 365, we apply the division lemma to 688 and 365, to get
688 = 365 x 1 + 323
Step 2: Since the reminder 365 ≠ 0, we apply division lemma to 323 and 365, to get
365 = 323 x 1 + 42
Step 3: We consider the new divisor 323 and the new remainder 42, and apply the division lemma to get
323 = 42 x 7 + 29
We consider the new divisor 42 and the new remainder 29,and apply the division lemma to get
42 = 29 x 1 + 13
We consider the new divisor 29 and the new remainder 13,and apply the division lemma to get
29 = 13 x 2 + 3
We consider the new divisor 13 and the new remainder 3,and apply the division lemma to get
13 = 3 x 4 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 688 and 365 is 1
Notice that 1 = HCF(3,1) = HCF(13,3) = HCF(29,13) = HCF(42,29) = HCF(323,42) = HCF(365,323) = HCF(688,365) .
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Frequently Asked Questions on HCF of 688, 365 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, 365?
Answer: HCF of 688, 365 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 688, 365 using Euclid's Algorithm?
Answer: For arbitrary numbers 688, 365 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.