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 680, 1445, 8235 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 680, 1445, 8235 is 5 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 680, 1445, 8235 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 680, 1445, 8235 is 5.
HCF(680, 1445, 8235) = 5
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 680, 1445, 8235 is 5.
Step 1: Since 1445 > 680, we apply the division lemma to 1445 and 680, to get
1445 = 680 x 2 + 85
Step 2: Since the reminder 680 ≠ 0, we apply division lemma to 85 and 680, to get
680 = 85 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 85, the HCF of 680 and 1445 is 85
Notice that 85 = HCF(680,85) = HCF(1445,680) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 8235 > 85, we apply the division lemma to 8235 and 85, to get
8235 = 85 x 96 + 75
Step 2: Since the reminder 85 ≠ 0, we apply division lemma to 75 and 85, to get
85 = 75 x 1 + 10
Step 3: We consider the new divisor 75 and the new remainder 10, and apply the division lemma to get
75 = 10 x 7 + 5
We consider the new divisor 10 and the new remainder 5, and apply the division lemma to get
10 = 5 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 85 and 8235 is 5
Notice that 5 = HCF(10,5) = HCF(75,10) = HCF(85,75) = HCF(8235,85) .
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 680, 1445, 8235?
Answer: HCF of 680, 1445, 8235 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 680, 1445, 8235 using Euclid's Algorithm?
Answer: For arbitrary numbers 680, 1445, 8235 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.