Highest Common Factor of 565, 910 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, 910 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 565, 910 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, 910 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, 910 is 5.
HCF(565, 910) = 5
HCF of 565, 910 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, 910 is 5.
Highest Common Factor of 565,910 is 5
Step 1: Since 910 > 565, we apply the division lemma to 910 and 565, to get
910 = 565 x 1 + 345
Step 2: Since the reminder 565 ≠ 0, we apply division lemma to 345 and 565, to get
565 = 345 x 1 + 220
Step 3: We consider the new divisor 345 and the new remainder 220, and apply the division lemma to get
345 = 220 x 1 + 125
We consider the new divisor 220 and the new remainder 125,and apply the division lemma to get
220 = 125 x 1 + 95
We consider the new divisor 125 and the new remainder 95,and apply the division lemma to get
125 = 95 x 1 + 30
We consider the new divisor 95 and the new remainder 30,and apply the division lemma to get
95 = 30 x 3 + 5
We consider the new divisor 30 and the new remainder 5,and apply the division lemma to get
30 = 5 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 565 and 910 is 5
Notice that 5 = HCF(30,5) = HCF(95,30) = HCF(125,95) = HCF(220,125) = HCF(345,220) = HCF(565,345) = HCF(910,565) .
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Frequently Asked Questions on HCF of 565, 910 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, 910?
Answer: HCF of 565, 910 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 565, 910 using Euclid's Algorithm?
Answer: For arbitrary numbers 565, 910 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.