Highest Common Factor of 312, 338, 142 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, 338, 142 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 312, 338, 142 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, 338, 142 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, 338, 142 is 2.
HCF(312, 338, 142) = 2
HCF of 312, 338, 142 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, 338, 142 is 2.
Highest Common Factor of 312,338,142 is 2
Step 1: Since 338 > 312, we apply the division lemma to 338 and 312, to get
338 = 312 x 1 + 26
Step 2: Since the reminder 312 ≠ 0, we apply division lemma to 26 and 312, to get
312 = 26 x 12 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 26, the HCF of 312 and 338 is 26
Notice that 26 = HCF(312,26) = HCF(338,312) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 142 > 26, we apply the division lemma to 142 and 26, to get
142 = 26 x 5 + 12
Step 2: Since the reminder 26 ≠ 0, we apply division lemma to 12 and 26, to get
26 = 12 x 2 + 2
Step 3: We consider the new divisor 12 and the new remainder 2, and apply the division lemma to get
12 = 2 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 26 and 142 is 2
Notice that 2 = HCF(12,2) = HCF(26,12) = HCF(142,26) .
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Frequently Asked Questions on HCF of 312, 338, 142 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, 338, 142?
Answer: HCF of 312, 338, 142 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 312, 338, 142 using Euclid's Algorithm?
Answer: For arbitrary numbers 312, 338, 142 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.