Highest Common Factor of 408, 969, 844 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 408, 969, 844 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 408, 969, 844 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 408, 969, 844 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 408, 969, 844 is 1.
HCF(408, 969, 844) = 1
HCF of 408, 969, 844 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 408, 969, 844 is 1.
Highest Common Factor of 408,969,844 is 1
Step 1: Since 969 > 408, we apply the division lemma to 969 and 408, to get
969 = 408 x 2 + 153
Step 2: Since the reminder 408 ≠ 0, we apply division lemma to 153 and 408, to get
408 = 153 x 2 + 102
Step 3: We consider the new divisor 153 and the new remainder 102, and apply the division lemma to get
153 = 102 x 1 + 51
We consider the new divisor 102 and the new remainder 51, and apply the division lemma to get
102 = 51 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 51, the HCF of 408 and 969 is 51
Notice that 51 = HCF(102,51) = HCF(153,102) = HCF(408,153) = HCF(969,408) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 844 > 51, we apply the division lemma to 844 and 51, to get
844 = 51 x 16 + 28
Step 2: Since the reminder 51 ≠ 0, we apply division lemma to 28 and 51, to get
51 = 28 x 1 + 23
Step 3: We consider the new divisor 28 and the new remainder 23, and apply the division lemma to get
28 = 23 x 1 + 5
We consider the new divisor 23 and the new remainder 5,and apply the division lemma to get
23 = 5 x 4 + 3
We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get
5 = 3 x 1 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
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 51 and 844 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(23,5) = HCF(28,23) = HCF(51,28) = HCF(844,51) .
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Frequently Asked Questions on HCF of 408, 969, 844 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 408, 969, 844?
Answer: HCF of 408, 969, 844 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 408, 969, 844 using Euclid's Algorithm?
Answer: For arbitrary numbers 408, 969, 844 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
