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, 4180, 6663 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 342, 4180, 6663 is 1 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, 4180, 6663 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, 4180, 6663 is 1.
HCF(342, 4180, 6663) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 342, 4180, 6663 is 1.
Step 1: Since 4180 > 342, we apply the division lemma to 4180 and 342, to get
4180 = 342 x 12 + 76
Step 2: Since the reminder 342 ≠ 0, we apply division lemma to 76 and 342, to get
342 = 76 x 4 + 38
Step 3: We consider the new divisor 76 and the new remainder 38, and apply the division lemma to get
76 = 38 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 38, the HCF of 342 and 4180 is 38
Notice that 38 = HCF(76,38) = HCF(342,76) = HCF(4180,342) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 6663 > 38, we apply the division lemma to 6663 and 38, to get
6663 = 38 x 175 + 13
Step 2: Since the reminder 38 ≠ 0, we apply division lemma to 13 and 38, to get
38 = 13 x 2 + 12
Step 3: We consider the new divisor 13 and the new remainder 12, and apply the division lemma to get
13 = 12 x 1 + 1
We consider the new divisor 12 and the new remainder 1, and apply the division lemma to get
12 = 1 x 12 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 38 and 6663 is 1
Notice that 1 = HCF(12,1) = HCF(13,12) = HCF(38,13) = HCF(6663,38) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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, 4180, 6663?
Answer: HCF of 342, 4180, 6663 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 342, 4180, 6663 using Euclid's Algorithm?
Answer: For arbitrary numbers 342, 4180, 6663 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.