Highest Common Factor of 60, 75, 55, 514 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, 75, 55, 514 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 60, 75, 55, 514 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, 75, 55, 514 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, 75, 55, 514 is 1.
HCF(60, 75, 55, 514) = 1
HCF of 60, 75, 55, 514 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, 75, 55, 514 is 1.
Highest Common Factor of 60,75,55,514 is 1
Step 1: Since 75 > 60, we apply the division lemma to 75 and 60, to get
75 = 60 x 1 + 15
Step 2: Since the reminder 60 ≠ 0, we apply division lemma to 15 and 60, to get
60 = 15 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 60 and 75 is 15
Notice that 15 = HCF(60,15) = HCF(75,60) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 55 > 15, we apply the division lemma to 55 and 15, to get
55 = 15 x 3 + 10
Step 2: Since the reminder 15 ≠ 0, we apply division lemma to 10 and 15, to get
15 = 10 x 1 + 5
Step 3: We consider the new divisor 10 and the new remainder 5, and apply the division lemma to get
10 = 5 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 15 and 55 is 5
Notice that 5 = HCF(10,5) = HCF(15,10) = HCF(55,15) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 514 > 5, we apply the division lemma to 514 and 5, to get
514 = 5 x 102 + 4
Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 4 and 5, to get
5 = 4 x 1 + 1
Step 3: We consider the new divisor 4 and the new remainder 1, and apply the division lemma 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 5 and 514 is 1
Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(514,5) .
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Frequently Asked Questions on HCF of 60, 75, 55, 514 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, 75, 55, 514?
Answer: HCF of 60, 75, 55, 514 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 60, 75, 55, 514 using Euclid's Algorithm?
Answer: For arbitrary numbers 60, 75, 55, 514 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.