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 911, 9470, 9006 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 911, 9470, 9006 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 911, 9470, 9006 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 911, 9470, 9006 is 1.
HCF(911, 9470, 9006) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 911, 9470, 9006 is 1.
Step 1: Since 9470 > 911, we apply the division lemma to 9470 and 911, to get
9470 = 911 x 10 + 360
Step 2: Since the reminder 911 ≠ 0, we apply division lemma to 360 and 911, to get
911 = 360 x 2 + 191
Step 3: We consider the new divisor 360 and the new remainder 191, and apply the division lemma to get
360 = 191 x 1 + 169
We consider the new divisor 191 and the new remainder 169,and apply the division lemma to get
191 = 169 x 1 + 22
We consider the new divisor 169 and the new remainder 22,and apply the division lemma to get
169 = 22 x 7 + 15
We consider the new divisor 22 and the new remainder 15,and apply the division lemma to get
22 = 15 x 1 + 7
We consider the new divisor 15 and the new remainder 7,and apply the division lemma to get
15 = 7 x 2 + 1
We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 911 and 9470 is 1
Notice that 1 = HCF(7,1) = HCF(15,7) = HCF(22,15) = HCF(169,22) = HCF(191,169) = HCF(360,191) = HCF(911,360) = HCF(9470,911) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 9006 > 1, we apply the division lemma to 9006 and 1, to get
9006 = 1 x 9006 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 9006 is 1
Notice that 1 = HCF(9006,1) .
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 911, 9470, 9006?
Answer: HCF of 911, 9470, 9006 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 911, 9470, 9006 using Euclid's Algorithm?
Answer: For arbitrary numbers 911, 9470, 9006 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.