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 9354, 9369, 67129 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 9354, 9369, 67129 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 9354, 9369, 67129 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 9354, 9369, 67129 is 1.
HCF(9354, 9369, 67129) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9354, 9369, 67129 is 1.
Step 1: Since 9369 > 9354, we apply the division lemma to 9369 and 9354, to get
9369 = 9354 x 1 + 15
Step 2: Since the reminder 9354 ≠ 0, we apply division lemma to 15 and 9354, to get
9354 = 15 x 623 + 9
Step 3: We consider the new divisor 15 and the new remainder 9, and apply the division lemma to get
15 = 9 x 1 + 6
We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get
9 = 6 x 1 + 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 9354 and 9369 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(15,9) = HCF(9354,15) = HCF(9369,9354) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 67129 > 3, we apply the division lemma to 67129 and 3, to get
67129 = 3 x 22376 + 1
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, 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 3 and 67129 is 1
Notice that 1 = HCF(3,1) = HCF(67129,3) .
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 9354, 9369, 67129?
Answer: HCF of 9354, 9369, 67129 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9354, 9369, 67129 using Euclid's Algorithm?
Answer: For arbitrary numbers 9354, 9369, 67129 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.