Highest Common Factor of 849, 408 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 849, 408 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 849, 408 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 849, 408 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 849, 408 is 3.
HCF(849, 408) = 3
HCF of 849, 408 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 849, 408 is 3.
Highest Common Factor of 849,408 is 3
Step 1: Since 849 > 408, we apply the division lemma to 849 and 408, to get
849 = 408 x 2 + 33
Step 2: Since the reminder 408 ≠ 0, we apply division lemma to 33 and 408, to get
408 = 33 x 12 + 12
Step 3: We consider the new divisor 33 and the new remainder 12, and apply the division lemma to get
33 = 12 x 2 + 9
We consider the new divisor 12 and the new remainder 9,and apply the division lemma to get
12 = 9 x 1 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 849 and 408 is 3
Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(33,12) = HCF(408,33) = HCF(849,408) .
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Frequently Asked Questions on HCF of 849, 408 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 849, 408?
Answer: HCF of 849, 408 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 849, 408 using Euclid's Algorithm?
Answer: For arbitrary numbers 849, 408 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.