Highest Common Factor of 645, 680 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 645, 680 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 645, 680 is 5 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 645, 680 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 645, 680 is 5.
HCF(645, 680) = 5
HCF of 645, 680 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 645, 680 is 5.
Highest Common Factor of 645,680 is 5
Step 1: Since 680 > 645, we apply the division lemma to 680 and 645, to get
680 = 645 x 1 + 35
Step 2: Since the reminder 645 ≠ 0, we apply division lemma to 35 and 645, to get
645 = 35 x 18 + 15
Step 3: We consider the new divisor 35 and the new remainder 15, and apply the division lemma to get
35 = 15 x 2 + 5
We consider the new divisor 15 and the new remainder 5, and apply the division lemma to get
15 = 5 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 645 and 680 is 5
Notice that 5 = HCF(15,5) = HCF(35,15) = HCF(645,35) = HCF(680,645) .
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Frequently Asked Questions on HCF of 645, 680 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 645, 680?
Answer: HCF of 645, 680 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 645, 680 using Euclid's Algorithm?
Answer: For arbitrary numbers 645, 680 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.