Highest Common Factor of 565, 774 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, 774 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 565, 774 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 565, 774 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, 774 is 1.
HCF(565, 774) = 1
HCF of 565, 774 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, 774 is 1.
Highest Common Factor of 565,774 is 1
Step 1: Since 774 > 565, we apply the division lemma to 774 and 565, to get
774 = 565 x 1 + 209
Step 2: Since the reminder 565 ≠ 0, we apply division lemma to 209 and 565, to get
565 = 209 x 2 + 147
Step 3: We consider the new divisor 209 and the new remainder 147, and apply the division lemma to get
209 = 147 x 1 + 62
We consider the new divisor 147 and the new remainder 62,and apply the division lemma to get
147 = 62 x 2 + 23
We consider the new divisor 62 and the new remainder 23,and apply the division lemma to get
62 = 23 x 2 + 16
We consider the new divisor 23 and the new remainder 16,and apply the division lemma to get
23 = 16 x 1 + 7
We consider the new divisor 16 and the new remainder 7,and apply the division lemma to get
16 = 7 x 2 + 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 565 and 774 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(16,7) = HCF(23,16) = HCF(62,23) = HCF(147,62) = HCF(209,147) = HCF(565,209) = HCF(774,565) .
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Frequently Asked Questions on HCF of 565, 774 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, 774?
Answer: HCF of 565, 774 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 565, 774 using Euclid's Algorithm?
Answer: For arbitrary numbers 565, 774 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.