Highest Common Factor of 320, 865, 42, 243 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 320, 865, 42, 243 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 320, 865, 42, 243 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 320, 865, 42, 243 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 320, 865, 42, 243 is 1.
HCF(320, 865, 42, 243) = 1
HCF of 320, 865, 42, 243 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 320, 865, 42, 243 is 1.
Highest Common Factor of 320,865,42,243 is 1
Step 1: Since 865 > 320, we apply the division lemma to 865 and 320, to get
865 = 320 x 2 + 225
Step 2: Since the reminder 320 ≠ 0, we apply division lemma to 225 and 320, to get
320 = 225 x 1 + 95
Step 3: We consider the new divisor 225 and the new remainder 95, and apply the division lemma to get
225 = 95 x 2 + 35
We consider the new divisor 95 and the new remainder 35,and apply the division lemma to get
95 = 35 x 2 + 25
We consider the new divisor 35 and the new remainder 25,and apply the division lemma to get
35 = 25 x 1 + 10
We consider the new divisor 25 and the new remainder 10,and apply the division lemma to get
25 = 10 x 2 + 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 320 and 865 is 5
Notice that 5 = HCF(10,5) = HCF(25,10) = HCF(35,25) = HCF(95,35) = HCF(225,95) = HCF(320,225) = HCF(865,320) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 42 > 5, we apply the division lemma to 42 and 5, to get
42 = 5 x 8 + 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 42 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(42,5) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 243 > 1, we apply the division lemma to 243 and 1, to get
243 = 1 x 243 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 243 is 1
Notice that 1 = HCF(243,1) .
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Frequently Asked Questions on HCF of 320, 865, 42, 243 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 320, 865, 42, 243?
Answer: HCF of 320, 865, 42, 243 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 320, 865, 42, 243 using Euclid's Algorithm?
Answer: For arbitrary numbers 320, 865, 42, 243 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.