Highest Common Factor of 672, 209, 845 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 672, 209, 845 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 672, 209, 845 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 672, 209, 845 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 672, 209, 845 is 1.
HCF(672, 209, 845) = 1
HCF of 672, 209, 845 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 672, 209, 845 is 1.
Highest Common Factor of 672,209,845 is 1
Step 1: Since 672 > 209, we apply the division lemma to 672 and 209, to get
672 = 209 x 3 + 45
Step 2: Since the reminder 209 ≠ 0, we apply division lemma to 45 and 209, to get
209 = 45 x 4 + 29
Step 3: We consider the new divisor 45 and the new remainder 29, and apply the division lemma to get
45 = 29 x 1 + 16
We consider the new divisor 29 and the new remainder 16,and apply the division lemma to get
29 = 16 x 1 + 13
We consider the new divisor 16 and the new remainder 13,and apply the division lemma to get
16 = 13 x 1 + 3
We consider the new divisor 13 and the new remainder 3,and apply the division lemma to get
13 = 3 x 4 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma 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 672 and 209 is 1
Notice that 1 = HCF(3,1) = HCF(13,3) = HCF(16,13) = HCF(29,16) = HCF(45,29) = HCF(209,45) = HCF(672,209) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 845 > 1, we apply the division lemma to 845 and 1, to get
845 = 1 x 845 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 845 is 1
Notice that 1 = HCF(845,1) .
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Frequently Asked Questions on HCF of 672, 209, 845 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 672, 209, 845?
Answer: HCF of 672, 209, 845 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 672, 209, 845 using Euclid's Algorithm?
Answer: For arbitrary numbers 672, 209, 845 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.