Highest Common Factor of 5175, 6720, 67853 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 5175, 6720, 67853 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 5175, 6720, 67853 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 5175, 6720, 67853 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 5175, 6720, 67853 is 1.
HCF(5175, 6720, 67853) = 1
HCF of 5175, 6720, 67853 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 5175, 6720, 67853 is 1.
Highest Common Factor of 5175,6720,67853 is 1
Step 1: Since 6720 > 5175, we apply the division lemma to 6720 and 5175, to get
6720 = 5175 x 1 + 1545
Step 2: Since the reminder 5175 ≠ 0, we apply division lemma to 1545 and 5175, to get
5175 = 1545 x 3 + 540
Step 3: We consider the new divisor 1545 and the new remainder 540, and apply the division lemma to get
1545 = 540 x 2 + 465
We consider the new divisor 540 and the new remainder 465,and apply the division lemma to get
540 = 465 x 1 + 75
We consider the new divisor 465 and the new remainder 75,and apply the division lemma to get
465 = 75 x 6 + 15
We consider the new divisor 75 and the new remainder 15,and apply the division lemma to get
75 = 15 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 5175 and 6720 is 15
Notice that 15 = HCF(75,15) = HCF(465,75) = HCF(540,465) = HCF(1545,540) = HCF(5175,1545) = HCF(6720,5175) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 67853 > 15, we apply the division lemma to 67853 and 15, to get
67853 = 15 x 4523 + 8
Step 2: Since the reminder 15 ≠ 0, we apply division lemma to 8 and 15, to get
15 = 8 x 1 + 7
Step 3: We consider the new divisor 8 and the new remainder 7, and apply the division lemma to get
8 = 7 x 1 + 1
We consider the new divisor 7 and the new remainder 1, and apply the division lemma to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 15 and 67853 is 1
Notice that 1 = HCF(7,1) = HCF(8,7) = HCF(15,8) = HCF(67853,15) .
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Frequently Asked Questions on HCF of 5175, 6720, 67853 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 5175, 6720, 67853?
Answer: HCF of 5175, 6720, 67853 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 5175, 6720, 67853 using Euclid's Algorithm?
Answer: For arbitrary numbers 5175, 6720, 67853 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.