Highest Common Factor of 309, 896, 217, 60 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, 896, 217, 60 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 309, 896, 217, 60 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, 896, 217, 60 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, 896, 217, 60 is 1.
HCF(309, 896, 217, 60) = 1
HCF of 309, 896, 217, 60 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, 896, 217, 60 is 1.
Highest Common Factor of 309,896,217,60 is 1
Step 1: Since 896 > 309, we apply the division lemma to 896 and 309, to get
896 = 309 x 2 + 278
Step 2: Since the reminder 309 ≠ 0, we apply division lemma to 278 and 309, to get
309 = 278 x 1 + 31
Step 3: We consider the new divisor 278 and the new remainder 31, and apply the division lemma to get
278 = 31 x 8 + 30
We consider the new divisor 31 and the new remainder 30,and apply the division lemma to get
31 = 30 x 1 + 1
We consider the new divisor 30 and the new remainder 1,and apply the division lemma to get
30 = 1 x 30 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 309 and 896 is 1
Notice that 1 = HCF(30,1) = HCF(31,30) = HCF(278,31) = HCF(309,278) = HCF(896,309) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 217 > 1, we apply the division lemma to 217 and 1, to get
217 = 1 x 217 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 217 is 1
Notice that 1 = HCF(217,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 60 > 1, we apply the division lemma to 60 and 1, to get
60 = 1 x 60 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 60 is 1
Notice that 1 = HCF(60,1) .
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Frequently Asked Questions on HCF of 309, 896, 217, 60 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, 896, 217, 60?
Answer: HCF of 309, 896, 217, 60 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 309, 896, 217, 60 using Euclid's Algorithm?
Answer: For arbitrary numbers 309, 896, 217, 60 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.