Highest Common Factor of 6616, 9568, 31375 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 6616, 9568, 31375 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 6616, 9568, 31375 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 6616, 9568, 31375 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 6616, 9568, 31375 is 1.
HCF(6616, 9568, 31375) = 1
HCF of 6616, 9568, 31375 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6616, 9568, 31375 is 1.
Highest Common Factor of 6616,9568,31375 is 1
Step 1: Since 9568 > 6616, we apply the division lemma to 9568 and 6616, to get
9568 = 6616 x 1 + 2952
Step 2: Since the reminder 6616 ≠ 0, we apply division lemma to 2952 and 6616, to get
6616 = 2952 x 2 + 712
Step 3: We consider the new divisor 2952 and the new remainder 712, and apply the division lemma to get
2952 = 712 x 4 + 104
We consider the new divisor 712 and the new remainder 104,and apply the division lemma to get
712 = 104 x 6 + 88
We consider the new divisor 104 and the new remainder 88,and apply the division lemma to get
104 = 88 x 1 + 16
We consider the new divisor 88 and the new remainder 16,and apply the division lemma to get
88 = 16 x 5 + 8
We consider the new divisor 16 and the new remainder 8,and apply the division lemma to get
16 = 8 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 6616 and 9568 is 8
Notice that 8 = HCF(16,8) = HCF(88,16) = HCF(104,88) = HCF(712,104) = HCF(2952,712) = HCF(6616,2952) = HCF(9568,6616) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 31375 > 8, we apply the division lemma to 31375 and 8, to get
31375 = 8 x 3921 + 7
Step 2: Since the reminder 8 ≠ 0, we apply division lemma to 7 and 8, to get
8 = 7 x 1 + 1
Step 3: We consider the new divisor 7 and the new remainder 1, and apply the division lemma to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 8 and 31375 is 1
Notice that 1 = HCF(7,1) = HCF(8,7) = HCF(31375,8) .
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Frequently Asked Questions on HCF of 6616, 9568, 31375 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 6616, 9568, 31375?
Answer: HCF of 6616, 9568, 31375 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6616, 9568, 31375 using Euclid's Algorithm?
Answer: For arbitrary numbers 6616, 9568, 31375 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.