Highest Common Factor of 704, 2238, 3001 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 704, 2238, 3001 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 704, 2238, 3001 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 704, 2238, 3001 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 704, 2238, 3001 is 1.
HCF(704, 2238, 3001) = 1
HCF of 704, 2238, 3001 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 704, 2238, 3001 is 1.
Highest Common Factor of 704,2238,3001 is 1
Step 1: Since 2238 > 704, we apply the division lemma to 2238 and 704, to get
2238 = 704 x 3 + 126
Step 2: Since the reminder 704 ≠ 0, we apply division lemma to 126 and 704, to get
704 = 126 x 5 + 74
Step 3: We consider the new divisor 126 and the new remainder 74, and apply the division lemma to get
126 = 74 x 1 + 52
We consider the new divisor 74 and the new remainder 52,and apply the division lemma to get
74 = 52 x 1 + 22
We consider the new divisor 52 and the new remainder 22,and apply the division lemma to get
52 = 22 x 2 + 8
We consider the new divisor 22 and the new remainder 8,and apply the division lemma to get
22 = 8 x 2 + 6
We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get
8 = 6 x 1 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 704 and 2238 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(22,8) = HCF(52,22) = HCF(74,52) = HCF(126,74) = HCF(704,126) = HCF(2238,704) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 3001 > 2, we apply the division lemma to 3001 and 2, to get
3001 = 2 x 1500 + 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 3001 is 1
Notice that 1 = HCF(2,1) = HCF(3001,2) .
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Frequently Asked Questions on HCF of 704, 2238, 3001 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 704, 2238, 3001?
Answer: HCF of 704, 2238, 3001 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 704, 2238, 3001 using Euclid's Algorithm?
Answer: For arbitrary numbers 704, 2238, 3001 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.