Highest Common Factor of 312, 234, 274 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 312, 234, 274 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 312, 234, 274 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 312, 234, 274 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 312, 234, 274 is 2.
HCF(312, 234, 274) = 2
HCF of 312, 234, 274 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 312, 234, 274 is 2.
Highest Common Factor of 312,234,274 is 2
Step 1: Since 312 > 234, we apply the division lemma to 312 and 234, to get
312 = 234 x 1 + 78
Step 2: Since the reminder 234 ≠ 0, we apply division lemma to 78 and 234, to get
234 = 78 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 78, the HCF of 312 and 234 is 78
Notice that 78 = HCF(234,78) = HCF(312,234) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 274 > 78, we apply the division lemma to 274 and 78, to get
274 = 78 x 3 + 40
Step 2: Since the reminder 78 ≠ 0, we apply division lemma to 40 and 78, to get
78 = 40 x 1 + 38
Step 3: We consider the new divisor 40 and the new remainder 38, and apply the division lemma to get
40 = 38 x 1 + 2
We consider the new divisor 38 and the new remainder 2, and apply the division lemma 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 78 and 274 is 2
Notice that 2 = HCF(38,2) = HCF(40,38) = HCF(78,40) = HCF(274,78) .
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Frequently Asked Questions on HCF of 312, 234, 274 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 312, 234, 274?
Answer: HCF of 312, 234, 274 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 312, 234, 274 using Euclid's Algorithm?
Answer: For arbitrary numbers 312, 234, 274 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.