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, 204, 975 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 680, 204, 975 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 680, 204, 975 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, 204, 975 is 1.
HCF(680, 204, 975) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 680, 204, 975 is 1.
Step 1: Since 680 > 204, we apply the division lemma to 680 and 204, to get
680 = 204 x 3 + 68
Step 2: Since the reminder 204 ≠ 0, we apply division lemma to 68 and 204, to get
204 = 68 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 68, the HCF of 680 and 204 is 68
Notice that 68 = HCF(204,68) = HCF(680,204) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 975 > 68, we apply the division lemma to 975 and 68, to get
975 = 68 x 14 + 23
Step 2: Since the reminder 68 ≠ 0, we apply division lemma to 23 and 68, to get
68 = 23 x 2 + 22
Step 3: We consider the new divisor 23 and the new remainder 22, and apply the division lemma to get
23 = 22 x 1 + 1
We consider the new divisor 22 and the new remainder 1, and apply the division lemma to get
22 = 1 x 22 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 68 and 975 is 1
Notice that 1 = HCF(22,1) = HCF(23,22) = HCF(68,23) = HCF(975,68) .
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, 204, 975?
Answer: HCF of 680, 204, 975 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 680, 204, 975 using Euclid's Algorithm?
Answer: For arbitrary numbers 680, 204, 975 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.