Highest Common Factor of 696, 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 696, 909 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 696, 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 696, 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 696, 909 is 3.
HCF(696, 909) = 3
HCF of 696, 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 696, 909 is 3.
Highest Common Factor of 696,909 is 3
Step 1: Since 909 > 696, we apply the division lemma to 909 and 696, to get
909 = 696 x 1 + 213
Step 2: Since the reminder 696 ≠ 0, we apply division lemma to 213 and 696, to get
696 = 213 x 3 + 57
Step 3: We consider the new divisor 213 and the new remainder 57, and apply the division lemma to get
213 = 57 x 3 + 42
We consider the new divisor 57 and the new remainder 42,and apply the division lemma to get
57 = 42 x 1 + 15
We consider the new divisor 42 and the new remainder 15,and apply the division lemma to get
42 = 15 x 2 + 12
We consider the new divisor 15 and the new remainder 12,and apply the division lemma to get
15 = 12 x 1 + 3
We consider the new divisor 12 and the new remainder 3,and apply the division lemma to get
12 = 3 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 696 and 909 is 3
Notice that 3 = HCF(12,3) = HCF(15,12) = HCF(42,15) = HCF(57,42) = HCF(213,57) = HCF(696,213) = HCF(909,696) .
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Frequently Asked Questions on HCF of 696, 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 696, 909?
Answer: HCF of 696, 909 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 696, 909 using Euclid's Algorithm?
Answer: For arbitrary numbers 696, 909 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.