Highest Common Factor of 770, 345, 274 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 770, 345, 274 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 770, 345, 274 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 770, 345, 274 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 770, 345, 274 is 1.
HCF(770, 345, 274) = 1
HCF of 770, 345, 274 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 770, 345, 274 is 1.
Highest Common Factor of 770,345,274 is 1
Step 1: Since 770 > 345, we apply the division lemma to 770 and 345, to get
770 = 345 x 2 + 80
Step 2: Since the reminder 345 ≠ 0, we apply division lemma to 80 and 345, to get
345 = 80 x 4 + 25
Step 3: We consider the new divisor 80 and the new remainder 25, and apply the division lemma to get
80 = 25 x 3 + 5
We consider the new divisor 25 and the new remainder 5, and apply the division lemma to get
25 = 5 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 770 and 345 is 5
Notice that 5 = HCF(25,5) = HCF(80,25) = HCF(345,80) = HCF(770,345) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 274 > 5, we apply the division lemma to 274 and 5, to get
274 = 5 x 54 + 4
Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 4 and 5, to get
5 = 4 x 1 + 1
Step 3: We consider the new divisor 4 and the new remainder 1, and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5 and 274 is 1
Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(274,5) .
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Frequently Asked Questions on HCF of 770, 345, 274 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 770, 345, 274?
Answer: HCF of 770, 345, 274 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 770, 345, 274 using Euclid's Algorithm?
Answer: For arbitrary numbers 770, 345, 274 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.