Highest Common Factor of 768, 67560 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 768, 67560 i.e. 24 the largest integer that leaves a remainder zero for all numbers.
HCF of 768, 67560 is 24 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 768, 67560 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 768, 67560 is 24.
HCF(768, 67560) = 24
HCF of 768, 67560 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 768, 67560 is 24.
Highest Common Factor of 768,67560 is 24
Step 1: Since 67560 > 768, we apply the division lemma to 67560 and 768, to get
67560 = 768 x 87 + 744
Step 2: Since the reminder 768 ≠ 0, we apply division lemma to 744 and 768, to get
768 = 744 x 1 + 24
Step 3: We consider the new divisor 744 and the new remainder 24, and apply the division lemma to get
744 = 24 x 31 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 24, the HCF of 768 and 67560 is 24
Notice that 24 = HCF(744,24) = HCF(768,744) = HCF(67560,768) .
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Frequently Asked Questions on HCF of 768, 67560 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 768, 67560?
Answer: HCF of 768, 67560 is 24 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 768, 67560 using Euclid's Algorithm?
Answer: For arbitrary numbers 768, 67560 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.