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 780, 284, 802, 65 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 780, 284, 802, 65 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 780, 284, 802, 65 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 780, 284, 802, 65 is 1.
HCF(780, 284, 802, 65) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 780, 284, 802, 65 is 1.
Step 1: Since 780 > 284, we apply the division lemma to 780 and 284, to get
780 = 284 x 2 + 212
Step 2: Since the reminder 284 ≠ 0, we apply division lemma to 212 and 284, to get
284 = 212 x 1 + 72
Step 3: We consider the new divisor 212 and the new remainder 72, and apply the division lemma to get
212 = 72 x 2 + 68
We consider the new divisor 72 and the new remainder 68,and apply the division lemma to get
72 = 68 x 1 + 4
We consider the new divisor 68 and the new remainder 4,and apply the division lemma to get
68 = 4 x 17 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 780 and 284 is 4
Notice that 4 = HCF(68,4) = HCF(72,68) = HCF(212,72) = HCF(284,212) = HCF(780,284) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 802 > 4, we apply the division lemma to 802 and 4, to get
802 = 4 x 200 + 2
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 4 and 802 is 2
Notice that 2 = HCF(4,2) = HCF(802,4) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 65 > 2, we apply the division lemma to 65 and 2, to get
65 = 2 x 32 + 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 65 is 1
Notice that 1 = HCF(2,1) = HCF(65,2) .
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 780, 284, 802, 65?
Answer: HCF of 780, 284, 802, 65 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 780, 284, 802, 65 using Euclid's Algorithm?
Answer: For arbitrary numbers 780, 284, 802, 65 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.