Highest Common Factor of 680, 67755 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 680, 67755 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 680, 67755 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 680, 67755 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 680, 67755 is 5.
HCF(680, 67755) = 5
HCF of 680, 67755 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 680, 67755 is 5.
Highest Common Factor of 680,67755 is 5
Step 1: Since 67755 > 680, we apply the division lemma to 67755 and 680, to get
67755 = 680 x 99 + 435
Step 2: Since the reminder 680 ≠ 0, we apply division lemma to 435 and 680, to get
680 = 435 x 1 + 245
Step 3: We consider the new divisor 435 and the new remainder 245, and apply the division lemma to get
435 = 245 x 1 + 190
We consider the new divisor 245 and the new remainder 190,and apply the division lemma to get
245 = 190 x 1 + 55
We consider the new divisor 190 and the new remainder 55,and apply the division lemma to get
190 = 55 x 3 + 25
We consider the new divisor 55 and the new remainder 25,and apply the division lemma to get
55 = 25 x 2 + 5
We consider the new divisor 25 and the new remainder 5,and apply the division lemma to get
25 = 5 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 680 and 67755 is 5
Notice that 5 = HCF(25,5) = HCF(55,25) = HCF(190,55) = HCF(245,190) = HCF(435,245) = HCF(680,435) = HCF(67755,680) .
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Frequently Asked Questions on HCF of 680, 67755 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 680, 67755?
Answer: HCF of 680, 67755 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 680, 67755 using Euclid's Algorithm?
Answer: For arbitrary numbers 680, 67755 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.