Highest Common Factor of 870, 412, 668, 592 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 870, 412, 668, 592 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 870, 412, 668, 592 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 870, 412, 668, 592 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 870, 412, 668, 592 is 2.
HCF(870, 412, 668, 592) = 2
HCF of 870, 412, 668, 592 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 870, 412, 668, 592 is 2.
Highest Common Factor of 870,412,668,592 is 2
Step 1: Since 870 > 412, we apply the division lemma to 870 and 412, to get
870 = 412 x 2 + 46
Step 2: Since the reminder 412 ≠ 0, we apply division lemma to 46 and 412, to get
412 = 46 x 8 + 44
Step 3: We consider the new divisor 46 and the new remainder 44, and apply the division lemma to get
46 = 44 x 1 + 2
We consider the new divisor 44 and the new remainder 2, and apply the division lemma to get
44 = 2 x 22 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 870 and 412 is 2
Notice that 2 = HCF(44,2) = HCF(46,44) = HCF(412,46) = HCF(870,412) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 668 > 2, we apply the division lemma to 668 and 2, to get
668 = 2 x 334 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 668 is 2
Notice that 2 = HCF(668,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 592 > 2, we apply the division lemma to 592 and 2, to get
592 = 2 x 296 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 592 is 2
Notice that 2 = HCF(592,2) .
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Frequently Asked Questions on HCF of 870, 412, 668, 592 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 870, 412, 668, 592?
Answer: HCF of 870, 412, 668, 592 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 870, 412, 668, 592 using Euclid's Algorithm?
Answer: For arbitrary numbers 870, 412, 668, 592 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.