Highest Common Factor of 824, 174, 38 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 824, 174, 38 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 824, 174, 38 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 824, 174, 38 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 824, 174, 38 is 2.
HCF(824, 174, 38) = 2
HCF of 824, 174, 38 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 824, 174, 38 is 2.
Highest Common Factor of 824,174,38 is 2
Step 1: Since 824 > 174, we apply the division lemma to 824 and 174, to get
824 = 174 x 4 + 128
Step 2: Since the reminder 174 ≠ 0, we apply division lemma to 128 and 174, to get
174 = 128 x 1 + 46
Step 3: We consider the new divisor 128 and the new remainder 46, and apply the division lemma to get
128 = 46 x 2 + 36
We consider the new divisor 46 and the new remainder 36,and apply the division lemma to get
46 = 36 x 1 + 10
We consider the new divisor 36 and the new remainder 10,and apply the division lemma to get
36 = 10 x 3 + 6
We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get
10 = 6 x 1 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma 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 824 and 174 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(36,10) = HCF(46,36) = HCF(128,46) = HCF(174,128) = HCF(824,174) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 38 > 2, we apply the division lemma to 38 and 2, to get
38 = 2 x 19 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 38 is 2
Notice that 2 = HCF(38,2) .
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Frequently Asked Questions on HCF of 824, 174, 38 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 824, 174, 38?
Answer: HCF of 824, 174, 38 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 824, 174, 38 using Euclid's Algorithm?
Answer: For arbitrary numbers 824, 174, 38 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.