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 5345, 9122, 23100 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 5345, 9122, 23100 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 5345, 9122, 23100 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 5345, 9122, 23100 is 1.
HCF(5345, 9122, 23100) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 5345, 9122, 23100 is 1.
Step 1: Since 9122 > 5345, we apply the division lemma to 9122 and 5345, to get
9122 = 5345 x 1 + 3777
Step 2: Since the reminder 5345 ≠ 0, we apply division lemma to 3777 and 5345, to get
5345 = 3777 x 1 + 1568
Step 3: We consider the new divisor 3777 and the new remainder 1568, and apply the division lemma to get
3777 = 1568 x 2 + 641
We consider the new divisor 1568 and the new remainder 641,and apply the division lemma to get
1568 = 641 x 2 + 286
We consider the new divisor 641 and the new remainder 286,and apply the division lemma to get
641 = 286 x 2 + 69
We consider the new divisor 286 and the new remainder 69,and apply the division lemma to get
286 = 69 x 4 + 10
We consider the new divisor 69 and the new remainder 10,and apply the division lemma to get
69 = 10 x 6 + 9
We consider the new divisor 10 and the new remainder 9,and apply the division lemma to get
10 = 9 x 1 + 1
We consider the new divisor 9 and the new remainder 1,and apply the division lemma to get
9 = 1 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5345 and 9122 is 1
Notice that 1 = HCF(9,1) = HCF(10,9) = HCF(69,10) = HCF(286,69) = HCF(641,286) = HCF(1568,641) = HCF(3777,1568) = HCF(5345,3777) = HCF(9122,5345) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 23100 > 1, we apply the division lemma to 23100 and 1, to get
23100 = 1 x 23100 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 23100 is 1
Notice that 1 = HCF(23100,1) .
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 5345, 9122, 23100?
Answer: HCF of 5345, 9122, 23100 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 5345, 9122, 23100 using Euclid's Algorithm?
Answer: For arbitrary numbers 5345, 9122, 23100 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.