Highest Common Factor of 174, 1122, 1957 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, 1122, 1957 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 174, 1122, 1957 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, 1122, 1957 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, 1122, 1957 is 1.
HCF(174, 1122, 1957) = 1
HCF of 174, 1122, 1957 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, 1122, 1957 is 1.
Highest Common Factor of 174,1122,1957 is 1
Step 1: Since 1122 > 174, we apply the division lemma to 1122 and 174, to get
1122 = 174 x 6 + 78
Step 2: Since the reminder 174 ≠ 0, we apply division lemma to 78 and 174, to get
174 = 78 x 2 + 18
Step 3: We consider the new divisor 78 and the new remainder 18, and apply the division lemma to get
78 = 18 x 4 + 6
We consider the new divisor 18 and the new remainder 6, and apply the division lemma to get
18 = 6 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 174 and 1122 is 6
Notice that 6 = HCF(18,6) = HCF(78,18) = HCF(174,78) = HCF(1122,174) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 1957 > 6, we apply the division lemma to 1957 and 6, to get
1957 = 6 x 326 + 1
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 1 and 6, to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 6 and 1957 is 1
Notice that 1 = HCF(6,1) = HCF(1957,6) .
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Frequently Asked Questions on HCF of 174, 1122, 1957 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, 1122, 1957?
Answer: HCF of 174, 1122, 1957 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 174, 1122, 1957 using Euclid's Algorithm?
Answer: For arbitrary numbers 174, 1122, 1957 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.