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 614, 846, 25 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 614, 846, 25 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 614, 846, 25 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 614, 846, 25 is 1.
HCF(614, 846, 25) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 614, 846, 25 is 1.
Step 1: Since 846 > 614, we apply the division lemma to 846 and 614, to get
846 = 614 x 1 + 232
Step 2: Since the reminder 614 ≠ 0, we apply division lemma to 232 and 614, to get
614 = 232 x 2 + 150
Step 3: We consider the new divisor 232 and the new remainder 150, and apply the division lemma to get
232 = 150 x 1 + 82
We consider the new divisor 150 and the new remainder 82,and apply the division lemma to get
150 = 82 x 1 + 68
We consider the new divisor 82 and the new remainder 68,and apply the division lemma to get
82 = 68 x 1 + 14
We consider the new divisor 68 and the new remainder 14,and apply the division lemma to get
68 = 14 x 4 + 12
We consider the new divisor 14 and the new remainder 12,and apply the division lemma to get
14 = 12 x 1 + 2
We consider the new divisor 12 and the new remainder 2,and apply the division lemma to get
12 = 2 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 614 and 846 is 2
Notice that 2 = HCF(12,2) = HCF(14,12) = HCF(68,14) = HCF(82,68) = HCF(150,82) = HCF(232,150) = HCF(614,232) = HCF(846,614) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 25 > 2, we apply the division lemma to 25 and 2, to get
25 = 2 x 12 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 25 is 1
Notice that 1 = HCF(2,1) = HCF(25,2) .
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 614, 846, 25?
Answer: HCF of 614, 846, 25 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 614, 846, 25 using Euclid's Algorithm?
Answer: For arbitrary numbers 614, 846, 25 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.