Highest Common Factor of 465, 612, 538 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 465, 612, 538 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 465, 612, 538 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 465, 612, 538 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 465, 612, 538 is 1.
HCF(465, 612, 538) = 1
HCF of 465, 612, 538 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 465, 612, 538 is 1.
Highest Common Factor of 465,612,538 is 1
Step 1: Since 612 > 465, we apply the division lemma to 612 and 465, to get
612 = 465 x 1 + 147
Step 2: Since the reminder 465 ≠ 0, we apply division lemma to 147 and 465, to get
465 = 147 x 3 + 24
Step 3: We consider the new divisor 147 and the new remainder 24, and apply the division lemma to get
147 = 24 x 6 + 3
We consider the new divisor 24 and the new remainder 3, and apply the division lemma to get
24 = 3 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 465 and 612 is 3
Notice that 3 = HCF(24,3) = HCF(147,24) = HCF(465,147) = HCF(612,465) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 538 > 3, we apply the division lemma to 538 and 3, to get
538 = 3 x 179 + 1
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 538 is 1
Notice that 1 = HCF(3,1) = HCF(538,3) .
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Frequently Asked Questions on HCF of 465, 612, 538 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 465, 612, 538?
Answer: HCF of 465, 612, 538 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 465, 612, 538 using Euclid's Algorithm?
Answer: For arbitrary numbers 465, 612, 538 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.