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 355, 215, 642 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 355, 215, 642 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 355, 215, 642 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 355, 215, 642 is 1.
HCF(355, 215, 642) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 355, 215, 642 is 1.
Step 1: Since 355 > 215, we apply the division lemma to 355 and 215, to get
355 = 215 x 1 + 140
Step 2: Since the reminder 215 ≠ 0, we apply division lemma to 140 and 215, to get
215 = 140 x 1 + 75
Step 3: We consider the new divisor 140 and the new remainder 75, and apply the division lemma to get
140 = 75 x 1 + 65
We consider the new divisor 75 and the new remainder 65,and apply the division lemma to get
75 = 65 x 1 + 10
We consider the new divisor 65 and the new remainder 10,and apply the division lemma to get
65 = 10 x 6 + 5
We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get
10 = 5 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 355 and 215 is 5
Notice that 5 = HCF(10,5) = HCF(65,10) = HCF(75,65) = HCF(140,75) = HCF(215,140) = HCF(355,215) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 642 > 5, we apply the division lemma to 642 and 5, to get
642 = 5 x 128 + 2
Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 2 and 5, to get
5 = 2 x 2 + 1
Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5 and 642 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(642,5) .
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 355, 215, 642?
Answer: HCF of 355, 215, 642 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 355, 215, 642 using Euclid's Algorithm?
Answer: For arbitrary numbers 355, 215, 642 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.