Highest Common Factor of 912, 209, 706 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 912, 209, 706 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 912, 209, 706 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 912, 209, 706 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 912, 209, 706 is 1.
HCF(912, 209, 706) = 1
HCF of 912, 209, 706 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 912, 209, 706 is 1.
Highest Common Factor of 912,209,706 is 1
Step 1: Since 912 > 209, we apply the division lemma to 912 and 209, to get
912 = 209 x 4 + 76
Step 2: Since the reminder 209 ≠ 0, we apply division lemma to 76 and 209, to get
209 = 76 x 2 + 57
Step 3: We consider the new divisor 76 and the new remainder 57, and apply the division lemma to get
76 = 57 x 1 + 19
We consider the new divisor 57 and the new remainder 19, and apply the division lemma to get
57 = 19 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 19, the HCF of 912 and 209 is 19
Notice that 19 = HCF(57,19) = HCF(76,57) = HCF(209,76) = HCF(912,209) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 706 > 19, we apply the division lemma to 706 and 19, to get
706 = 19 x 37 + 3
Step 2: Since the reminder 19 ≠ 0, we apply division lemma to 3 and 19, to get
19 = 3 x 6 + 1
Step 3: We consider the new divisor 3 and the new remainder 1, and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 19 and 706 is 1
Notice that 1 = HCF(3,1) = HCF(19,3) = HCF(706,19) .
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Frequently Asked Questions on HCF of 912, 209, 706 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 912, 209, 706?
Answer: HCF of 912, 209, 706 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 912, 209, 706 using Euclid's Algorithm?
Answer: For arbitrary numbers 912, 209, 706 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.