Highest Common Factor of 174, 584, 842, 44 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 174, 584, 842, 44 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 174, 584, 842, 44 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 174, 584, 842, 44 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 174, 584, 842, 44 is 2.
HCF(174, 584, 842, 44) = 2
HCF of 174, 584, 842, 44 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 174, 584, 842, 44 is 2.
Highest Common Factor of 174,584,842,44 is 2
Step 1: Since 584 > 174, we apply the division lemma to 584 and 174, to get
584 = 174 x 3 + 62
Step 2: Since the reminder 174 ≠ 0, we apply division lemma to 62 and 174, to get
174 = 62 x 2 + 50
Step 3: We consider the new divisor 62 and the new remainder 50, and apply the division lemma to get
62 = 50 x 1 + 12
We consider the new divisor 50 and the new remainder 12,and apply the division lemma to get
50 = 12 x 4 + 2
We consider the new divisor 12 and the new remainder 2,and apply the division lemma to get
12 = 2 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 174 and 584 is 2
Notice that 2 = HCF(12,2) = HCF(50,12) = HCF(62,50) = HCF(174,62) = HCF(584,174) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 842 > 2, we apply the division lemma to 842 and 2, to get
842 = 2 x 421 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 842 is 2
Notice that 2 = HCF(842,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 44 > 2, we apply the division lemma to 44 and 2, 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 2 and 44 is 2
Notice that 2 = HCF(44,2) .
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Frequently Asked Questions on HCF of 174, 584, 842, 44 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 174, 584, 842, 44?
Answer: HCF of 174, 584, 842, 44 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 174, 584, 842, 44 using Euclid's Algorithm?
Answer: For arbitrary numbers 174, 584, 842, 44 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.