Highest Common Factor of 307, 448, 102, 680 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 307, 448, 102, 680 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 307, 448, 102, 680 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 307, 448, 102, 680 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 307, 448, 102, 680 is 1.
HCF(307, 448, 102, 680) = 1
HCF of 307, 448, 102, 680 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 307, 448, 102, 680 is 1.
Highest Common Factor of 307,448,102,680 is 1
Step 1: Since 448 > 307, we apply the division lemma to 448 and 307, to get
448 = 307 x 1 + 141
Step 2: Since the reminder 307 ≠ 0, we apply division lemma to 141 and 307, to get
307 = 141 x 2 + 25
Step 3: We consider the new divisor 141 and the new remainder 25, and apply the division lemma to get
141 = 25 x 5 + 16
We consider the new divisor 25 and the new remainder 16,and apply the division lemma to get
25 = 16 x 1 + 9
We consider the new divisor 16 and the new remainder 9,and apply the division lemma to get
16 = 9 x 1 + 7
We consider the new divisor 9 and the new remainder 7,and apply the division lemma to get
9 = 7 x 1 + 2
We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get
7 = 2 x 3 + 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 307 and 448 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(9,7) = HCF(16,9) = HCF(25,16) = HCF(141,25) = HCF(307,141) = HCF(448,307) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 102 > 1, we apply the division lemma to 102 and 1, to get
102 = 1 x 102 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 102 is 1
Notice that 1 = HCF(102,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 680 > 1, we apply the division lemma to 680 and 1, to get
680 = 1 x 680 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 680 is 1
Notice that 1 = HCF(680,1) .
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Frequently Asked Questions on HCF of 307, 448, 102, 680 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 307, 448, 102, 680?
Answer: HCF of 307, 448, 102, 680 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 307, 448, 102, 680 using Euclid's Algorithm?
Answer: For arbitrary numbers 307, 448, 102, 680 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.