Highest Common Factor of 465, 596, 74 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, 596, 74 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 465, 596, 74 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, 596, 74 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, 596, 74 is 1.
HCF(465, 596, 74) = 1
HCF of 465, 596, 74 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, 596, 74 is 1.
Highest Common Factor of 465,596,74 is 1
Step 1: Since 596 > 465, we apply the division lemma to 596 and 465, to get
596 = 465 x 1 + 131
Step 2: Since the reminder 465 ≠ 0, we apply division lemma to 131 and 465, to get
465 = 131 x 3 + 72
Step 3: We consider the new divisor 131 and the new remainder 72, and apply the division lemma to get
131 = 72 x 1 + 59
We consider the new divisor 72 and the new remainder 59,and apply the division lemma to get
72 = 59 x 1 + 13
We consider the new divisor 59 and the new remainder 13,and apply the division lemma to get
59 = 13 x 4 + 7
We consider the new divisor 13 and the new remainder 7,and apply the division lemma to get
13 = 7 x 1 + 6
We consider the new divisor 7 and the new remainder 6,and apply the division lemma to get
7 = 6 x 1 + 1
We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 465 and 596 is 1
Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(13,7) = HCF(59,13) = HCF(72,59) = HCF(131,72) = HCF(465,131) = HCF(596,465) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 74 > 1, we apply the division lemma to 74 and 1, to get
74 = 1 x 74 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 74 is 1
Notice that 1 = HCF(74,1) .
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Frequently Asked Questions on HCF of 465, 596, 74 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, 596, 74?
Answer: HCF of 465, 596, 74 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 465, 596, 74 using Euclid's Algorithm?
Answer: For arbitrary numbers 465, 596, 74 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.