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 512, 2973, 9022 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 512, 2973, 9022 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 512, 2973, 9022 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 512, 2973, 9022 is 1.
HCF(512, 2973, 9022) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 512, 2973, 9022 is 1.
Step 1: Since 2973 > 512, we apply the division lemma to 2973 and 512, to get
2973 = 512 x 5 + 413
Step 2: Since the reminder 512 ≠ 0, we apply division lemma to 413 and 512, to get
512 = 413 x 1 + 99
Step 3: We consider the new divisor 413 and the new remainder 99, and apply the division lemma to get
413 = 99 x 4 + 17
We consider the new divisor 99 and the new remainder 17,and apply the division lemma to get
99 = 17 x 5 + 14
We consider the new divisor 17 and the new remainder 14,and apply the division lemma to get
17 = 14 x 1 + 3
We consider the new divisor 14 and the new remainder 3,and apply the division lemma to get
14 = 3 x 4 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 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 512 and 2973 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(14,3) = HCF(17,14) = HCF(99,17) = HCF(413,99) = HCF(512,413) = HCF(2973,512) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 9022 > 1, we apply the division lemma to 9022 and 1, to get
9022 = 1 x 9022 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 9022 is 1
Notice that 1 = HCF(9022,1) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 512, 2973, 9022?
Answer: HCF of 512, 2973, 9022 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 512, 2973, 9022 using Euclid's Algorithm?
Answer: For arbitrary numbers 512, 2973, 9022 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.