Highest Common Factor of 807, 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 807, 912 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 807, 912 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 807, 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 807, 912 is 3.
HCF(807, 912) = 3
HCF of 807, 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 807, 912 is 3.
Highest Common Factor of 807,912 is 3
Step 1: Since 912 > 807, we apply the division lemma to 912 and 807, to get
912 = 807 x 1 + 105
Step 2: Since the reminder 807 ≠ 0, we apply division lemma to 105 and 807, to get
807 = 105 x 7 + 72
Step 3: We consider the new divisor 105 and the new remainder 72, and apply the division lemma to get
105 = 72 x 1 + 33
We consider the new divisor 72 and the new remainder 33,and apply the division lemma to get
72 = 33 x 2 + 6
We consider the new divisor 33 and the new remainder 6,and apply the division lemma to get
33 = 6 x 5 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 807 and 912 is 3
Notice that 3 = HCF(6,3) = HCF(33,6) = HCF(72,33) = HCF(105,72) = HCF(807,105) = HCF(912,807) .
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Frequently Asked Questions on HCF of 807, 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 807, 912?
Answer: HCF of 807, 912 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 807, 912 using Euclid's Algorithm?
Answer: For arbitrary numbers 807, 912 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.