Highest Common Factor of 477, 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 477, 912 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 477, 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 477, 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 477, 912 is 3.
HCF(477, 912) = 3
HCF of 477, 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 477, 912 is 3.
Highest Common Factor of 477,912 is 3
Step 1: Since 912 > 477, we apply the division lemma to 912 and 477, to get
912 = 477 x 1 + 435
Step 2: Since the reminder 477 ≠ 0, we apply division lemma to 435 and 477, to get
477 = 435 x 1 + 42
Step 3: We consider the new divisor 435 and the new remainder 42, and apply the division lemma to get
435 = 42 x 10 + 15
We consider the new divisor 42 and the new remainder 15,and apply the division lemma to get
42 = 15 x 2 + 12
We consider the new divisor 15 and the new remainder 12,and apply the division lemma to get
15 = 12 x 1 + 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 477 and 912 is 3
Notice that 3 = HCF(12,3) = HCF(15,12) = HCF(42,15) = HCF(435,42) = HCF(477,435) = HCF(912,477) .
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Frequently Asked Questions on HCF of 477, 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 477, 912?
Answer: HCF of 477, 912 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 477, 912 using Euclid's Algorithm?
Answer: For arbitrary numbers 477, 912 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.