Highest Common Factor of 213, 177, 909 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 213, 177, 909 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 213, 177, 909 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 213, 177, 909 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 213, 177, 909 is 3.
HCF(213, 177, 909) = 3
HCF of 213, 177, 909 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 213, 177, 909 is 3.
Highest Common Factor of 213,177,909 is 3
Step 1: Since 213 > 177, we apply the division lemma to 213 and 177, to get
213 = 177 x 1 + 36
Step 2: Since the reminder 177 ≠ 0, we apply division lemma to 36 and 177, to get
177 = 36 x 4 + 33
Step 3: We consider the new divisor 36 and the new remainder 33, and apply the division lemma to get
36 = 33 x 1 + 3
We consider the new divisor 33 and the new remainder 3, and apply the division lemma to get
33 = 3 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 213 and 177 is 3
Notice that 3 = HCF(33,3) = HCF(36,33) = HCF(177,36) = HCF(213,177) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 909 > 3, we apply the division lemma to 909 and 3, to get
909 = 3 x 303 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 909 is 3
Notice that 3 = HCF(909,3) .
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Frequently Asked Questions on HCF of 213, 177, 909 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 213, 177, 909?
Answer: HCF of 213, 177, 909 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 213, 177, 909 using Euclid's Algorithm?
Answer: For arbitrary numbers 213, 177, 909 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
