Highest Common Factor of 561, 309, 686, 192 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 561, 309, 686, 192 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 561, 309, 686, 192 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 561, 309, 686, 192 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 561, 309, 686, 192 is 1.
HCF(561, 309, 686, 192) = 1
HCF of 561, 309, 686, 192 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 561, 309, 686, 192 is 1.
Highest Common Factor of 561,309,686,192 is 1
Step 1: Since 561 > 309, we apply the division lemma to 561 and 309, to get
561 = 309 x 1 + 252
Step 2: Since the reminder 309 ≠ 0, we apply division lemma to 252 and 309, to get
309 = 252 x 1 + 57
Step 3: We consider the new divisor 252 and the new remainder 57, and apply the division lemma to get
252 = 57 x 4 + 24
We consider the new divisor 57 and the new remainder 24,and apply the division lemma to get
57 = 24 x 2 + 9
We consider the new divisor 24 and the new remainder 9,and apply the division lemma to get
24 = 9 x 2 + 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 561 and 309 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(24,9) = HCF(57,24) = HCF(252,57) = HCF(309,252) = HCF(561,309) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 686 > 3, we apply the division lemma to 686 and 3, to get
686 = 3 x 228 + 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 686 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(686,3) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 192 > 1, we apply the division lemma to 192 and 1, to get
192 = 1 x 192 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 192 is 1
Notice that 1 = HCF(192,1) .
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Frequently Asked Questions on HCF of 561, 309, 686, 192 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 561, 309, 686, 192?
Answer: HCF of 561, 309, 686, 192 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 561, 309, 686, 192 using Euclid's Algorithm?
Answer: For arbitrary numbers 561, 309, 686, 192 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.