Highest Common Factor of 6765, 1760 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 6765, 1760 i.e. 55 the largest integer that leaves a remainder zero for all numbers.
HCF of 6765, 1760 is 55 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 6765, 1760 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 6765, 1760 is 55.
HCF(6765, 1760) = 55
HCF of 6765, 1760 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6765, 1760 is 55.
Highest Common Factor of 6765,1760 is 55
Step 1: Since 6765 > 1760, we apply the division lemma to 6765 and 1760, to get
6765 = 1760 x 3 + 1485
Step 2: Since the reminder 1760 ≠ 0, we apply division lemma to 1485 and 1760, to get
1760 = 1485 x 1 + 275
Step 3: We consider the new divisor 1485 and the new remainder 275, and apply the division lemma to get
1485 = 275 x 5 + 110
We consider the new divisor 275 and the new remainder 110,and apply the division lemma to get
275 = 110 x 2 + 55
We consider the new divisor 110 and the new remainder 55,and apply the division lemma to get
110 = 55 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 55, the HCF of 6765 and 1760 is 55
Notice that 55 = HCF(110,55) = HCF(275,110) = HCF(1485,275) = HCF(1760,1485) = HCF(6765,1760) .
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Frequently Asked Questions on HCF of 6765, 1760 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 6765, 1760?
Answer: HCF of 6765, 1760 is 55 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6765, 1760 using Euclid's Algorithm?
Answer: For arbitrary numbers 6765, 1760 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.