Highest Common Factor of 596, 2152, 8070 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 596, 2152, 8070 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 596, 2152, 8070 is 2 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 596, 2152, 8070 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 596, 2152, 8070 is 2.
HCF(596, 2152, 8070) = 2
HCF of 596, 2152, 8070 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 596, 2152, 8070 is 2.
Highest Common Factor of 596,2152,8070 is 2
Step 1: Since 2152 > 596, we apply the division lemma to 2152 and 596, to get
2152 = 596 x 3 + 364
Step 2: Since the reminder 596 ≠ 0, we apply division lemma to 364 and 596, to get
596 = 364 x 1 + 232
Step 3: We consider the new divisor 364 and the new remainder 232, and apply the division lemma to get
364 = 232 x 1 + 132
We consider the new divisor 232 and the new remainder 132,and apply the division lemma to get
232 = 132 x 1 + 100
We consider the new divisor 132 and the new remainder 100,and apply the division lemma to get
132 = 100 x 1 + 32
We consider the new divisor 100 and the new remainder 32,and apply the division lemma to get
100 = 32 x 3 + 4
We consider the new divisor 32 and the new remainder 4,and apply the division lemma to get
32 = 4 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 596 and 2152 is 4
Notice that 4 = HCF(32,4) = HCF(100,32) = HCF(132,100) = HCF(232,132) = HCF(364,232) = HCF(596,364) = HCF(2152,596) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 8070 > 4, we apply the division lemma to 8070 and 4, to get
8070 = 4 x 2017 + 2
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 4 and 8070 is 2
Notice that 2 = HCF(4,2) = HCF(8070,4) .
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Frequently Asked Questions on HCF of 596, 2152, 8070 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 596, 2152, 8070?
Answer: HCF of 596, 2152, 8070 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 596, 2152, 8070 using Euclid's Algorithm?
Answer: For arbitrary numbers 596, 2152, 8070 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
