Highest Common Factor of 174, 237 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, 237 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 174, 237 is 3 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, 237 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, 237 is 3.
HCF(174, 237) = 3
HCF of 174, 237 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, 237 is 3.
Highest Common Factor of 174,237 is 3
Step 1: Since 237 > 174, we apply the division lemma to 237 and 174, to get
237 = 174 x 1 + 63
Step 2: Since the reminder 174 ≠ 0, we apply division lemma to 63 and 174, to get
174 = 63 x 2 + 48
Step 3: We consider the new divisor 63 and the new remainder 48, and apply the division lemma to get
63 = 48 x 1 + 15
We consider the new divisor 48 and the new remainder 15,and apply the division lemma to get
48 = 15 x 3 + 3
We consider the new divisor 15 and the new remainder 3,and apply the division lemma to get
15 = 3 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 174 and 237 is 3
Notice that 3 = HCF(15,3) = HCF(48,15) = HCF(63,48) = HCF(174,63) = HCF(237,174) .
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Frequently Asked Questions on HCF of 174, 237 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, 237?
Answer: HCF of 174, 237 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 174, 237 using Euclid's Algorithm?
Answer: For arbitrary numbers 174, 237 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.