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 3602, 4085, 21955 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 3602, 4085, 21955 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 3602, 4085, 21955 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 3602, 4085, 21955 is 1.
HCF(3602, 4085, 21955) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 3602, 4085, 21955 is 1.
Step 1: Since 4085 > 3602, we apply the division lemma to 4085 and 3602, to get
4085 = 3602 x 1 + 483
Step 2: Since the reminder 3602 ≠ 0, we apply division lemma to 483 and 3602, to get
3602 = 483 x 7 + 221
Step 3: We consider the new divisor 483 and the new remainder 221, and apply the division lemma to get
483 = 221 x 2 + 41
We consider the new divisor 221 and the new remainder 41,and apply the division lemma to get
221 = 41 x 5 + 16
We consider the new divisor 41 and the new remainder 16,and apply the division lemma to get
41 = 16 x 2 + 9
We consider the new divisor 16 and the new remainder 9,and apply the division lemma to get
16 = 9 x 1 + 7
We consider the new divisor 9 and the new remainder 7,and apply the division lemma to get
9 = 7 x 1 + 2
We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get
7 = 2 x 3 + 1
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 3602 and 4085 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(9,7) = HCF(16,9) = HCF(41,16) = HCF(221,41) = HCF(483,221) = HCF(3602,483) = HCF(4085,3602) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 21955 > 1, we apply the division lemma to 21955 and 1, to get
21955 = 1 x 21955 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 21955 is 1
Notice that 1 = HCF(21955,1) .
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 3602, 4085, 21955?
Answer: HCF of 3602, 4085, 21955 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 3602, 4085, 21955 using Euclid's Algorithm?
Answer: For arbitrary numbers 3602, 4085, 21955 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.