Highest Common Factor of 342, 67047 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 342, 67047 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 342, 67047 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 342, 67047 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 342, 67047 is 3.
HCF(342, 67047) = 3
HCF of 342, 67047 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 342, 67047 is 3.
Highest Common Factor of 342,67047 is 3
Step 1: Since 67047 > 342, we apply the division lemma to 67047 and 342, to get
67047 = 342 x 196 + 15
Step 2: Since the reminder 342 ≠ 0, we apply division lemma to 15 and 342, to get
342 = 15 x 22 + 12
Step 3: We consider the new divisor 15 and the new remainder 12, and apply the division lemma to get
15 = 12 x 1 + 3
We consider the new divisor 12 and the new remainder 3, and apply the division lemma to get
12 = 3 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 342 and 67047 is 3
Notice that 3 = HCF(12,3) = HCF(15,12) = HCF(342,15) = HCF(67047,342) .
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Frequently Asked Questions on HCF of 342, 67047 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 342, 67047?
Answer: HCF of 342, 67047 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 342, 67047 using Euclid's Algorithm?
Answer: For arbitrary numbers 342, 67047 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.