Highest Common Factor of 362, 2205, 8961 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 362, 2205, 8961 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 362, 2205, 8961 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 362, 2205, 8961 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 362, 2205, 8961 is 1.
HCF(362, 2205, 8961) = 1
HCF of 362, 2205, 8961 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 362, 2205, 8961 is 1.
Highest Common Factor of 362,2205,8961 is 1
Step 1: Since 2205 > 362, we apply the division lemma to 2205 and 362, to get
2205 = 362 x 6 + 33
Step 2: Since the reminder 362 ≠ 0, we apply division lemma to 33 and 362, to get
362 = 33 x 10 + 32
Step 3: We consider the new divisor 33 and the new remainder 32, and apply the division lemma to get
33 = 32 x 1 + 1
We consider the new divisor 32 and the new remainder 1, and apply the division lemma to get
32 = 1 x 32 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 362 and 2205 is 1
Notice that 1 = HCF(32,1) = HCF(33,32) = HCF(362,33) = HCF(2205,362) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 8961 > 1, we apply the division lemma to 8961 and 1, to get
8961 = 1 x 8961 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 8961 is 1
Notice that 1 = HCF(8961,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 362, 2205, 8961 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 362, 2205, 8961?
Answer: HCF of 362, 2205, 8961 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 362, 2205, 8961 using Euclid's Algorithm?
Answer: For arbitrary numbers 362, 2205, 8961 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.