Highest Common Factor of 648, 814, 969, 331 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 648, 814, 969, 331 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 648, 814, 969, 331 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 648, 814, 969, 331 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 648, 814, 969, 331 is 1.
HCF(648, 814, 969, 331) = 1
HCF of 648, 814, 969, 331 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 648, 814, 969, 331 is 1.
Highest Common Factor of 648,814,969,331 is 1
Step 1: Since 814 > 648, we apply the division lemma to 814 and 648, to get
814 = 648 x 1 + 166
Step 2: Since the reminder 648 ≠ 0, we apply division lemma to 166 and 648, to get
648 = 166 x 3 + 150
Step 3: We consider the new divisor 166 and the new remainder 150, and apply the division lemma to get
166 = 150 x 1 + 16
We consider the new divisor 150 and the new remainder 16,and apply the division lemma to get
150 = 16 x 9 + 6
We consider the new divisor 16 and the new remainder 6,and apply the division lemma to get
16 = 6 x 2 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 648 and 814 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(16,6) = HCF(150,16) = HCF(166,150) = HCF(648,166) = HCF(814,648) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 969 > 2, we apply the division lemma to 969 and 2, to get
969 = 2 x 484 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 969 is 1
Notice that 1 = HCF(2,1) = HCF(969,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 331 > 1, we apply the division lemma to 331 and 1, to get
331 = 1 x 331 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 331 is 1
Notice that 1 = HCF(331,1) .
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Frequently Asked Questions on HCF of 648, 814, 969, 331 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 648, 814, 969, 331?
Answer: HCF of 648, 814, 969, 331 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 648, 814, 969, 331 using Euclid's Algorithm?
Answer: For arbitrary numbers 648, 814, 969, 331 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.