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 907, 2453, 8505 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 907, 2453, 8505 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 907, 2453, 8505 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 907, 2453, 8505 is 1.
HCF(907, 2453, 8505) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 907, 2453, 8505 is 1.
Step 1: Since 2453 > 907, we apply the division lemma to 2453 and 907, to get
2453 = 907 x 2 + 639
Step 2: Since the reminder 907 ≠ 0, we apply division lemma to 639 and 907, to get
907 = 639 x 1 + 268
Step 3: We consider the new divisor 639 and the new remainder 268, and apply the division lemma to get
639 = 268 x 2 + 103
We consider the new divisor 268 and the new remainder 103,and apply the division lemma to get
268 = 103 x 2 + 62
We consider the new divisor 103 and the new remainder 62,and apply the division lemma to get
103 = 62 x 1 + 41
We consider the new divisor 62 and the new remainder 41,and apply the division lemma to get
62 = 41 x 1 + 21
We consider the new divisor 41 and the new remainder 21,and apply the division lemma to get
41 = 21 x 1 + 20
We consider the new divisor 21 and the new remainder 20,and apply the division lemma to get
21 = 20 x 1 + 1
We consider the new divisor 20 and the new remainder 1,and apply the division lemma to get
20 = 1 x 20 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 907 and 2453 is 1
Notice that 1 = HCF(20,1) = HCF(21,20) = HCF(41,21) = HCF(62,41) = HCF(103,62) = HCF(268,103) = HCF(639,268) = HCF(907,639) = HCF(2453,907) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 8505 > 1, we apply the division lemma to 8505 and 1, to get
8505 = 1 x 8505 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 8505 is 1
Notice that 1 = HCF(8505,1) .
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 907, 2453, 8505?
Answer: HCF of 907, 2453, 8505 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 907, 2453, 8505 using Euclid's Algorithm?
Answer: For arbitrary numbers 907, 2453, 8505 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.