Highest Common Factor of 716, 860, 65 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 716, 860, 65 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 716, 860, 65 is 1 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 716, 860, 65 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 716, 860, 65 is 1.
HCF(716, 860, 65) = 1
HCF of 716, 860, 65 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 716, 860, 65 is 1.
Highest Common Factor of 716,860,65 is 1
Step 1: Since 860 > 716, we apply the division lemma to 860 and 716, to get
860 = 716 x 1 + 144
Step 2: Since the reminder 716 ≠ 0, we apply division lemma to 144 and 716, to get
716 = 144 x 4 + 140
Step 3: We consider the new divisor 144 and the new remainder 140, and apply the division lemma to get
144 = 140 x 1 + 4
We consider the new divisor 140 and the new remainder 4, and apply the division lemma to get
140 = 4 x 35 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 716 and 860 is 4
Notice that 4 = HCF(140,4) = HCF(144,140) = HCF(716,144) = HCF(860,716) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 65 > 4, we apply the division lemma to 65 and 4, to get
65 = 4 x 16 + 1
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 1 and 4, to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 4 and 65 is 1
Notice that 1 = HCF(4,1) = HCF(65,4) .
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Frequently Asked Questions on HCF of 716, 860, 65 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 716, 860, 65?
Answer: HCF of 716, 860, 65 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 716, 860, 65 using Euclid's Algorithm?
Answer: For arbitrary numbers 716, 860, 65 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.