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 909, 675, 101, 523 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 909, 675, 101, 523 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 909, 675, 101, 523 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 909, 675, 101, 523 is 1.
HCF(909, 675, 101, 523) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 909, 675, 101, 523 is 1.
Step 1: Since 909 > 675, we apply the division lemma to 909 and 675, to get
909 = 675 x 1 + 234
Step 2: Since the reminder 675 ≠ 0, we apply division lemma to 234 and 675, to get
675 = 234 x 2 + 207
Step 3: We consider the new divisor 234 and the new remainder 207, and apply the division lemma to get
234 = 207 x 1 + 27
We consider the new divisor 207 and the new remainder 27,and apply the division lemma to get
207 = 27 x 7 + 18
We consider the new divisor 27 and the new remainder 18,and apply the division lemma to get
27 = 18 x 1 + 9
We consider the new divisor 18 and the new remainder 9,and apply the division lemma to get
18 = 9 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 909 and 675 is 9
Notice that 9 = HCF(18,9) = HCF(27,18) = HCF(207,27) = HCF(234,207) = HCF(675,234) = HCF(909,675) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 101 > 9, we apply the division lemma to 101 and 9, to get
101 = 9 x 11 + 2
Step 2: Since the reminder 9 ≠ 0, we apply division lemma to 2 and 9, to get
9 = 2 x 4 + 1
Step 3: 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 9 and 101 is 1
Notice that 1 = HCF(2,1) = HCF(9,2) = HCF(101,9) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 523 > 1, we apply the division lemma to 523 and 1, to get
523 = 1 x 523 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 523 is 1
Notice that 1 = HCF(523,1) .
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 909, 675, 101, 523?
Answer: HCF of 909, 675, 101, 523 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 909, 675, 101, 523 using Euclid's Algorithm?
Answer: For arbitrary numbers 909, 675, 101, 523 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.