Highest Common Factor of 357, 582, 83, 622 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 357, 582, 83, 622 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 357, 582, 83, 622 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 357, 582, 83, 622 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 357, 582, 83, 622 is 1.
HCF(357, 582, 83, 622) = 1
HCF of 357, 582, 83, 622 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 357, 582, 83, 622 is 1.
Highest Common Factor of 357,582,83,622 is 1
Step 1: Since 582 > 357, we apply the division lemma to 582 and 357, to get
582 = 357 x 1 + 225
Step 2: Since the reminder 357 ≠ 0, we apply division lemma to 225 and 357, to get
357 = 225 x 1 + 132
Step 3: We consider the new divisor 225 and the new remainder 132, and apply the division lemma to get
225 = 132 x 1 + 93
We consider the new divisor 132 and the new remainder 93,and apply the division lemma to get
132 = 93 x 1 + 39
We consider the new divisor 93 and the new remainder 39,and apply the division lemma to get
93 = 39 x 2 + 15
We consider the new divisor 39 and the new remainder 15,and apply the division lemma to get
39 = 15 x 2 + 9
We consider the new divisor 15 and the new remainder 9,and apply the division lemma to get
15 = 9 x 1 + 6
We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get
9 = 6 x 1 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 357 and 582 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(15,9) = HCF(39,15) = HCF(93,39) = HCF(132,93) = HCF(225,132) = HCF(357,225) = HCF(582,357) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 83 > 3, we apply the division lemma to 83 and 3, to get
83 = 3 x 27 + 2
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get
3 = 2 x 1 + 1
Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 83 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(83,3) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 622 > 1, we apply the division lemma to 622 and 1, to get
622 = 1 x 622 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 622 is 1
Notice that 1 = HCF(622,1) .
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Frequently Asked Questions on HCF of 357, 582, 83, 622 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 357, 582, 83, 622?
Answer: HCF of 357, 582, 83, 622 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 357, 582, 83, 622 using Euclid's Algorithm?
Answer: For arbitrary numbers 357, 582, 83, 622 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.