Highest Common Factor of 309, 861, 281, 57 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 309, 861, 281, 57 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 309, 861, 281, 57 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 309, 861, 281, 57 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 309, 861, 281, 57 is 1.
HCF(309, 861, 281, 57) = 1
HCF of 309, 861, 281, 57 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 309, 861, 281, 57 is 1.
Highest Common Factor of 309,861,281,57 is 1
Step 1: Since 861 > 309, we apply the division lemma to 861 and 309, to get
861 = 309 x 2 + 243
Step 2: Since the reminder 309 ≠ 0, we apply division lemma to 243 and 309, to get
309 = 243 x 1 + 66
Step 3: We consider the new divisor 243 and the new remainder 66, and apply the division lemma to get
243 = 66 x 3 + 45
We consider the new divisor 66 and the new remainder 45,and apply the division lemma to get
66 = 45 x 1 + 21
We consider the new divisor 45 and the new remainder 21,and apply the division lemma to get
45 = 21 x 2 + 3
We consider the new divisor 21 and the new remainder 3,and apply the division lemma to get
21 = 3 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 309 and 861 is 3
Notice that 3 = HCF(21,3) = HCF(45,21) = HCF(66,45) = HCF(243,66) = HCF(309,243) = HCF(861,309) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 281 > 3, we apply the division lemma to 281 and 3, to get
281 = 3 x 93 + 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 281 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(281,3) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 57 > 1, we apply the division lemma to 57 and 1, to get
57 = 1 x 57 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 57 is 1
Notice that 1 = HCF(57,1) .
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Frequently Asked Questions on HCF of 309, 861, 281, 57 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 309, 861, 281, 57?
Answer: HCF of 309, 861, 281, 57 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 309, 861, 281, 57 using Euclid's Algorithm?
Answer: For arbitrary numbers 309, 861, 281, 57 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.