Highest Common Factor of 126, 234 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 126, 234 i.e. 18 the largest integer that leaves a remainder zero for all numbers.
HCF of 126, 234 is 18 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 126, 234 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 126, 234 is 18.
HCF(126, 234) = 18
HCF of 126, 234 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 126, 234 is 18.
Highest Common Factor of 126,234 is 18
Step 1: Since 234 > 126, we apply the division lemma to 234 and 126, to get
234 = 126 x 1 + 108
Step 2: Since the reminder 126 ≠ 0, we apply division lemma to 108 and 126, to get
126 = 108 x 1 + 18
Step 3: We consider the new divisor 108 and the new remainder 18, and apply the division lemma to get
108 = 18 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 18, the HCF of 126 and 234 is 18
Notice that 18 = HCF(108,18) = HCF(126,108) = HCF(234,126) .
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Frequently Asked Questions on HCF of 126, 234 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 126, 234?
Answer: HCF of 126, 234 is 18 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 126, 234 using Euclid's Algorithm?
Answer: For arbitrary numbers 126, 234 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.