Highest Common Factor of 60, 84, 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 60, 84, 65 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 60, 84, 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 60, 84, 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 60, 84, 65 is 1.
HCF(60, 84, 65) = 1
HCF of 60, 84, 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 60, 84, 65 is 1.
Highest Common Factor of 60,84,65 is 1
Step 1: Since 84 > 60, we apply the division lemma to 84 and 60, to get
84 = 60 x 1 + 24
Step 2: Since the reminder 60 ≠ 0, we apply division lemma to 24 and 60, to get
60 = 24 x 2 + 12
Step 3: We consider the new divisor 24 and the new remainder 12, and apply the division lemma to get
24 = 12 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 60 and 84 is 12
Notice that 12 = HCF(24,12) = HCF(60,24) = HCF(84,60) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 65 > 12, we apply the division lemma to 65 and 12, to get
65 = 12 x 5 + 5
Step 2: Since the reminder 12 ≠ 0, we apply division lemma to 5 and 12, to get
12 = 5 x 2 + 2
Step 3: We consider the new divisor 5 and the new remainder 2, and apply the division lemma to get
5 = 2 x 2 + 1
We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 12 and 65 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(12,5) = HCF(65,12) .
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Frequently Asked Questions on HCF of 60, 84, 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 60, 84, 65?
Answer: HCF of 60, 84, 65 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 60, 84, 65 using Euclid's Algorithm?
Answer: For arbitrary numbers 60, 84, 65 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.