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 765, 476, 768 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 765, 476, 768 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 765, 476, 768 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 765, 476, 768 is 1.
HCF(765, 476, 768) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 765, 476, 768 is 1.
Step 1: Since 765 > 476, we apply the division lemma to 765 and 476, to get
765 = 476 x 1 + 289
Step 2: Since the reminder 476 ≠ 0, we apply division lemma to 289 and 476, to get
476 = 289 x 1 + 187
Step 3: We consider the new divisor 289 and the new remainder 187, and apply the division lemma to get
289 = 187 x 1 + 102
We consider the new divisor 187 and the new remainder 102,and apply the division lemma to get
187 = 102 x 1 + 85
We consider the new divisor 102 and the new remainder 85,and apply the division lemma to get
102 = 85 x 1 + 17
We consider the new divisor 85 and the new remainder 17,and apply the division lemma to get
85 = 17 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 17, the HCF of 765 and 476 is 17
Notice that 17 = HCF(85,17) = HCF(102,85) = HCF(187,102) = HCF(289,187) = HCF(476,289) = HCF(765,476) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 768 > 17, we apply the division lemma to 768 and 17, to get
768 = 17 x 45 + 3
Step 2: Since the reminder 17 ≠ 0, we apply division lemma to 3 and 17, to get
17 = 3 x 5 + 2
Step 3: We consider the new divisor 3 and the new remainder 2, and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1, and apply the division lemma 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 17 and 768 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(17,3) = HCF(768,17) .
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 765, 476, 768?
Answer: HCF of 765, 476, 768 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 765, 476, 768 using Euclid's Algorithm?
Answer: For arbitrary numbers 765, 476, 768 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.