Highest Common Factor of 565, 6735, 2195 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 565, 6735, 2195 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 565, 6735, 2195 is 5 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 565, 6735, 2195 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 565, 6735, 2195 is 5.
HCF(565, 6735, 2195) = 5
HCF of 565, 6735, 2195 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 565, 6735, 2195 is 5.
Highest Common Factor of 565,6735,2195 is 5
Step 1: Since 6735 > 565, we apply the division lemma to 6735 and 565, to get
6735 = 565 x 11 + 520
Step 2: Since the reminder 565 ≠ 0, we apply division lemma to 520 and 565, to get
565 = 520 x 1 + 45
Step 3: We consider the new divisor 520 and the new remainder 45, and apply the division lemma to get
520 = 45 x 11 + 25
We consider the new divisor 45 and the new remainder 25,and apply the division lemma to get
45 = 25 x 1 + 20
We consider the new divisor 25 and the new remainder 20,and apply the division lemma to get
25 = 20 x 1 + 5
We consider the new divisor 20 and the new remainder 5,and apply the division lemma to get
20 = 5 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 565 and 6735 is 5
Notice that 5 = HCF(20,5) = HCF(25,20) = HCF(45,25) = HCF(520,45) = HCF(565,520) = HCF(6735,565) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 2195 > 5, we apply the division lemma to 2195 and 5, to get
2195 = 5 x 439 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 5 and 2195 is 5
Notice that 5 = HCF(2195,5) .
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Frequently Asked Questions on HCF of 565, 6735, 2195 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 565, 6735, 2195?
Answer: HCF of 565, 6735, 2195 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 565, 6735, 2195 using Euclid's Algorithm?
Answer: For arbitrary numbers 565, 6735, 2195 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.