Highest Common Factor of 74, 345, 704 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 74, 345, 704 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 74, 345, 704 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 74, 345, 704 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 74, 345, 704 is 1.
HCF(74, 345, 704) = 1
HCF of 74, 345, 704 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 74, 345, 704 is 1.
Highest Common Factor of 74,345,704 is 1
Step 1: Since 345 > 74, we apply the division lemma to 345 and 74, to get
345 = 74 x 4 + 49
Step 2: Since the reminder 74 ≠ 0, we apply division lemma to 49 and 74, to get
74 = 49 x 1 + 25
Step 3: We consider the new divisor 49 and the new remainder 25, and apply the division lemma to get
49 = 25 x 1 + 24
We consider the new divisor 25 and the new remainder 24,and apply the division lemma to get
25 = 24 x 1 + 1
We consider the new divisor 24 and the new remainder 1,and apply the division lemma to get
24 = 1 x 24 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 74 and 345 is 1
Notice that 1 = HCF(24,1) = HCF(25,24) = HCF(49,25) = HCF(74,49) = HCF(345,74) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 704 > 1, we apply the division lemma to 704 and 1, to get
704 = 1 x 704 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 704 is 1
Notice that 1 = HCF(704,1) .
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Frequently Asked Questions on HCF of 74, 345, 704 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 74, 345, 704?
Answer: HCF of 74, 345, 704 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 74, 345, 704 using Euclid's Algorithm?
Answer: For arbitrary numbers 74, 345, 704 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.