Highest Common Factor of 609, 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 609, 774 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 609, 774 is 3 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 609, 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 609, 774 is 3.
HCF(609, 774) = 3
HCF of 609, 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 609, 774 is 3.
Highest Common Factor of 609,774 is 3
Step 1: Since 774 > 609, we apply the division lemma to 774 and 609, to get
774 = 609 x 1 + 165
Step 2: Since the reminder 609 ≠ 0, we apply division lemma to 165 and 609, to get
609 = 165 x 3 + 114
Step 3: We consider the new divisor 165 and the new remainder 114, and apply the division lemma to get
165 = 114 x 1 + 51
We consider the new divisor 114 and the new remainder 51,and apply the division lemma to get
114 = 51 x 2 + 12
We consider the new divisor 51 and the new remainder 12,and apply the division lemma to get
51 = 12 x 4 + 3
We consider the new divisor 12 and the new remainder 3,and apply the division lemma to get
12 = 3 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 609 and 774 is 3
Notice that 3 = HCF(12,3) = HCF(51,12) = HCF(114,51) = HCF(165,114) = HCF(609,165) = HCF(774,609) .
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Frequently Asked Questions on HCF of 609, 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 609, 774?
Answer: HCF of 609, 774 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 609, 774 using Euclid's Algorithm?
Answer: For arbitrary numbers 609, 774 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.