Highest Common Factor of 342, 660, 105, 339 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, 660, 105, 339 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 342, 660, 105, 339 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, 660, 105, 339 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, 660, 105, 339 is 3.
HCF(342, 660, 105, 339) = 3
HCF of 342, 660, 105, 339 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, 660, 105, 339 is 3.
Highest Common Factor of 342,660,105,339 is 3
Step 1: Since 660 > 342, we apply the division lemma to 660 and 342, to get
660 = 342 x 1 + 318
Step 2: Since the reminder 342 ≠ 0, we apply division lemma to 318 and 342, to get
342 = 318 x 1 + 24
Step 3: We consider the new divisor 318 and the new remainder 24, and apply the division lemma to get
318 = 24 x 13 + 6
We consider the new divisor 24 and the new remainder 6, and apply the division lemma to get
24 = 6 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 342 and 660 is 6
Notice that 6 = HCF(24,6) = HCF(318,24) = HCF(342,318) = HCF(660,342) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 105 > 6, we apply the division lemma to 105 and 6, to get
105 = 6 x 17 + 3
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 3 and 6, to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 6 and 105 is 3
Notice that 3 = HCF(6,3) = HCF(105,6) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 339 > 3, we apply the division lemma to 339 and 3, to get
339 = 3 x 113 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 339 is 3
Notice that 3 = HCF(339,3) .
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Frequently Asked Questions on HCF of 342, 660, 105, 339 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, 660, 105, 339?
Answer: HCF of 342, 660, 105, 339 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 342, 660, 105, 339 using Euclid's Algorithm?
Answer: For arbitrary numbers 342, 660, 105, 339 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.