Highest Common Factor of 584, 452, 259, 17 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 584, 452, 259, 17 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 584, 452, 259, 17 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 584, 452, 259, 17 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 584, 452, 259, 17 is 1.
HCF(584, 452, 259, 17) = 1
HCF of 584, 452, 259, 17 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 584, 452, 259, 17 is 1.
Highest Common Factor of 584,452,259,17 is 1
Step 1: Since 584 > 452, we apply the division lemma to 584 and 452, to get
584 = 452 x 1 + 132
Step 2: Since the reminder 452 ≠ 0, we apply division lemma to 132 and 452, to get
452 = 132 x 3 + 56
Step 3: We consider the new divisor 132 and the new remainder 56, and apply the division lemma to get
132 = 56 x 2 + 20
We consider the new divisor 56 and the new remainder 20,and apply the division lemma to get
56 = 20 x 2 + 16
We consider the new divisor 20 and the new remainder 16,and apply the division lemma to get
20 = 16 x 1 + 4
We consider the new divisor 16 and the new remainder 4,and apply the division lemma to get
16 = 4 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 584 and 452 is 4
Notice that 4 = HCF(16,4) = HCF(20,16) = HCF(56,20) = HCF(132,56) = HCF(452,132) = HCF(584,452) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 259 > 4, we apply the division lemma to 259 and 4, to get
259 = 4 x 64 + 3
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 3 and 4, to get
4 = 3 x 1 + 1
Step 3: We consider the new divisor 3 and the new remainder 1, and apply the division lemma 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 4 and 259 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(259,4) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 17 > 1, we apply the division lemma to 17 and 1, to get
17 = 1 x 17 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 17 is 1
Notice that 1 = HCF(17,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 584, 452, 259, 17 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 584, 452, 259, 17?
Answer: HCF of 584, 452, 259, 17 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 584, 452, 259, 17 using Euclid's Algorithm?
Answer: For arbitrary numbers 584, 452, 259, 17 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.