Highest Common Factor of 274, 715, 506, 78 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 274, 715, 506, 78 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 274, 715, 506, 78 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 274, 715, 506, 78 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 274, 715, 506, 78 is 1.
HCF(274, 715, 506, 78) = 1
HCF of 274, 715, 506, 78 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 274, 715, 506, 78 is 1.
Highest Common Factor of 274,715,506,78 is 1
Step 1: Since 715 > 274, we apply the division lemma to 715 and 274, to get
715 = 274 x 2 + 167
Step 2: Since the reminder 274 ≠ 0, we apply division lemma to 167 and 274, to get
274 = 167 x 1 + 107
Step 3: We consider the new divisor 167 and the new remainder 107, and apply the division lemma to get
167 = 107 x 1 + 60
We consider the new divisor 107 and the new remainder 60,and apply the division lemma to get
107 = 60 x 1 + 47
We consider the new divisor 60 and the new remainder 47,and apply the division lemma to get
60 = 47 x 1 + 13
We consider the new divisor 47 and the new remainder 13,and apply the division lemma to get
47 = 13 x 3 + 8
We consider the new divisor 13 and the new remainder 8,and apply the division lemma to get
13 = 8 x 1 + 5
We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get
8 = 5 x 1 + 3
We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get
5 = 3 x 1 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 274 and 715 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(13,8) = HCF(47,13) = HCF(60,47) = HCF(107,60) = HCF(167,107) = HCF(274,167) = HCF(715,274) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 506 > 1, we apply the division lemma to 506 and 1, to get
506 = 1 x 506 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 506 is 1
Notice that 1 = HCF(506,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 78 > 1, we apply the division lemma to 78 and 1, to get
78 = 1 x 78 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 78 is 1
Notice that 1 = HCF(78,1) .
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Frequently Asked Questions on HCF of 274, 715, 506, 78 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 274, 715, 506, 78?
Answer: HCF of 274, 715, 506, 78 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 274, 715, 506, 78 using Euclid's Algorithm?
Answer: For arbitrary numbers 274, 715, 506, 78 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.