Highest Common Factor of 648, 407, 673, 68 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, 407, 673, 68 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 648, 407, 673, 68 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, 407, 673, 68 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, 407, 673, 68 is 1.
HCF(648, 407, 673, 68) = 1
HCF of 648, 407, 673, 68 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, 407, 673, 68 is 1.
Highest Common Factor of 648,407,673,68 is 1
Step 1: Since 648 > 407, we apply the division lemma to 648 and 407, to get
648 = 407 x 1 + 241
Step 2: Since the reminder 407 ≠ 0, we apply division lemma to 241 and 407, to get
407 = 241 x 1 + 166
Step 3: We consider the new divisor 241 and the new remainder 166, and apply the division lemma to get
241 = 166 x 1 + 75
We consider the new divisor 166 and the new remainder 75,and apply the division lemma to get
166 = 75 x 2 + 16
We consider the new divisor 75 and the new remainder 16,and apply the division lemma to get
75 = 16 x 4 + 11
We consider the new divisor 16 and the new remainder 11,and apply the division lemma to get
16 = 11 x 1 + 5
We consider the new divisor 11 and the new remainder 5,and apply the division lemma to get
11 = 5 x 2 + 1
We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 648 and 407 is 1
Notice that 1 = HCF(5,1) = HCF(11,5) = HCF(16,11) = HCF(75,16) = HCF(166,75) = HCF(241,166) = HCF(407,241) = HCF(648,407) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 673 > 1, we apply the division lemma to 673 and 1, to get
673 = 1 x 673 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 673 is 1
Notice that 1 = HCF(673,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 68 > 1, we apply the division lemma to 68 and 1, to get
68 = 1 x 68 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 68 is 1
Notice that 1 = HCF(68,1) .
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Frequently Asked Questions on HCF of 648, 407, 673, 68 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, 407, 673, 68?
Answer: HCF of 648, 407, 673, 68 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 648, 407, 673, 68 using Euclid's Algorithm?
Answer: For arbitrary numbers 648, 407, 673, 68 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.