Highest Common Factor of 600, 100, 765 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 600, 100, 765 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 600, 100, 765 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 600, 100, 765 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 600, 100, 765 is 5.
HCF(600, 100, 765) = 5
HCF of 600, 100, 765 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 600, 100, 765 is 5.
Highest Common Factor of 600,100,765 is 5
Step 1: Since 600 > 100, we apply the division lemma to 600 and 100, to get
600 = 100 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 100, the HCF of 600 and 100 is 100
Notice that 100 = HCF(600,100) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 765 > 100, we apply the division lemma to 765 and 100, to get
765 = 100 x 7 + 65
Step 2: Since the reminder 100 ≠ 0, we apply division lemma to 65 and 100, to get
100 = 65 x 1 + 35
Step 3: We consider the new divisor 65 and the new remainder 35, and apply the division lemma to get
65 = 35 x 1 + 30
We consider the new divisor 35 and the new remainder 30,and apply the division lemma to get
35 = 30 x 1 + 5
We consider the new divisor 30 and the new remainder 5,and apply the division lemma to get
30 = 5 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 100 and 765 is 5
Notice that 5 = HCF(30,5) = HCF(35,30) = HCF(65,35) = HCF(100,65) = HCF(765,100) .
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Frequently Asked Questions on HCF of 600, 100, 765 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 600, 100, 765?
Answer: HCF of 600, 100, 765 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 600, 100, 765 using Euclid's Algorithm?
Answer: For arbitrary numbers 600, 100, 765 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.