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 9572, 8341, 31010 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 9572, 8341, 31010 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 9572, 8341, 31010 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 9572, 8341, 31010 is 1.
HCF(9572, 8341, 31010) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9572, 8341, 31010 is 1.
Step 1: Since 9572 > 8341, we apply the division lemma to 9572 and 8341, to get
9572 = 8341 x 1 + 1231
Step 2: Since the reminder 8341 ≠ 0, we apply division lemma to 1231 and 8341, to get
8341 = 1231 x 6 + 955
Step 3: We consider the new divisor 1231 and the new remainder 955, and apply the division lemma to get
1231 = 955 x 1 + 276
We consider the new divisor 955 and the new remainder 276,and apply the division lemma to get
955 = 276 x 3 + 127
We consider the new divisor 276 and the new remainder 127,and apply the division lemma to get
276 = 127 x 2 + 22
We consider the new divisor 127 and the new remainder 22,and apply the division lemma to get
127 = 22 x 5 + 17
We consider the new divisor 22 and the new remainder 17,and apply the division lemma to get
22 = 17 x 1 + 5
We consider the new divisor 17 and the new remainder 5,and apply the division lemma to get
17 = 5 x 3 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 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 9572 and 8341 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(17,5) = HCF(22,17) = HCF(127,22) = HCF(276,127) = HCF(955,276) = HCF(1231,955) = HCF(8341,1231) = HCF(9572,8341) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 31010 > 1, we apply the division lemma to 31010 and 1, to get
31010 = 1 x 31010 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 31010 is 1
Notice that 1 = HCF(31010,1) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 9572, 8341, 31010?
Answer: HCF of 9572, 8341, 31010 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9572, 8341, 31010 using Euclid's Algorithm?
Answer: For arbitrary numbers 9572, 8341, 31010 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.