Highest Common Factor of 795, 660, 111 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 795, 660, 111 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 795, 660, 111 is 3 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 795, 660, 111 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 795, 660, 111 is 3.
HCF(795, 660, 111) = 3
HCF of 795, 660, 111 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 795, 660, 111 is 3.
Highest Common Factor of 795,660,111 is 3
Step 1: Since 795 > 660, we apply the division lemma to 795 and 660, to get
795 = 660 x 1 + 135
Step 2: Since the reminder 660 ≠ 0, we apply division lemma to 135 and 660, to get
660 = 135 x 4 + 120
Step 3: We consider the new divisor 135 and the new remainder 120, and apply the division lemma to get
135 = 120 x 1 + 15
We consider the new divisor 120 and the new remainder 15, and apply the division lemma to get
120 = 15 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 795 and 660 is 15
Notice that 15 = HCF(120,15) = HCF(135,120) = HCF(660,135) = HCF(795,660) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 111 > 15, we apply the division lemma to 111 and 15, to get
111 = 15 x 7 + 6
Step 2: Since the reminder 15 ≠ 0, we apply division lemma to 6 and 15, to get
15 = 6 x 2 + 3
Step 3: We consider the new divisor 6 and the new remainder 3, and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 15 and 111 is 3
Notice that 3 = HCF(6,3) = HCF(15,6) = HCF(111,15) .
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Frequently Asked Questions on HCF of 795, 660, 111 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 795, 660, 111?
Answer: HCF of 795, 660, 111 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 795, 660, 111 using Euclid's Algorithm?
Answer: For arbitrary numbers 795, 660, 111 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.