Highest Common Factor of 174, 870, 973 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, 870, 973 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 174, 870, 973 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 174, 870, 973 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, 870, 973 is 1.
HCF(174, 870, 973) = 1
HCF of 174, 870, 973 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, 870, 973 is 1.
Highest Common Factor of 174,870,973 is 1
Step 1: Since 870 > 174, we apply the division lemma to 870 and 174, to get
870 = 174 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 174, the HCF of 174 and 870 is 174
Notice that 174 = HCF(870,174) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 973 > 174, we apply the division lemma to 973 and 174, to get
973 = 174 x 5 + 103
Step 2: Since the reminder 174 ≠ 0, we apply division lemma to 103 and 174, to get
174 = 103 x 1 + 71
Step 3: We consider the new divisor 103 and the new remainder 71, and apply the division lemma to get
103 = 71 x 1 + 32
We consider the new divisor 71 and the new remainder 32,and apply the division lemma to get
71 = 32 x 2 + 7
We consider the new divisor 32 and the new remainder 7,and apply the division lemma to get
32 = 7 x 4 + 4
We consider the new divisor 7 and the new remainder 4,and apply the division lemma to get
7 = 4 x 1 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 174 and 973 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(32,7) = HCF(71,32) = HCF(103,71) = HCF(174,103) = HCF(973,174) .
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Frequently Asked Questions on HCF of 174, 870, 973 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, 870, 973?
Answer: HCF of 174, 870, 973 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 174, 870, 973 using Euclid's Algorithm?
Answer: For arbitrary numbers 174, 870, 973 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.