Highest Common Factor of 209, 774, 912 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 209, 774, 912 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 209, 774, 912 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 209, 774, 912 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 209, 774, 912 is 1.
HCF(209, 774, 912) = 1
HCF of 209, 774, 912 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 209, 774, 912 is 1.
Highest Common Factor of 209,774,912 is 1
Step 1: Since 774 > 209, we apply the division lemma to 774 and 209, to get
774 = 209 x 3 + 147
Step 2: Since the reminder 209 ≠ 0, we apply division lemma to 147 and 209, to get
209 = 147 x 1 + 62
Step 3: 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 209 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(774,209) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 912 > 1, we apply the division lemma to 912 and 1, to get
912 = 1 x 912 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 912 is 1
Notice that 1 = HCF(912,1) .
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Frequently Asked Questions on HCF of 209, 774, 912 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 209, 774, 912?
Answer: HCF of 209, 774, 912 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 209, 774, 912 using Euclid's Algorithm?
Answer: For arbitrary numbers 209, 774, 912 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
