Highest Common Factor of 416, 765 using Euclid's algorithm
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 416, 765 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 416, 765 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 416, 765 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 416, 765 is 1.
HCF(416, 765) = 1
HCF of 416, 765 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 416, 765 is 1.
Highest Common Factor of 416,765 is 1
Step 1: Since 765 > 416, we apply the division lemma to 765 and 416, to get
765 = 416 x 1 + 349
Step 2: Since the reminder 416 ≠ 0, we apply division lemma to 349 and 416, to get
416 = 349 x 1 + 67
Step 3: We consider the new divisor 349 and the new remainder 67, and apply the division lemma to get
349 = 67 x 5 + 14
We consider the new divisor 67 and the new remainder 14,and apply the division lemma to get
67 = 14 x 4 + 11
We consider the new divisor 14 and the new remainder 11,and apply the division lemma to get
14 = 11 x 1 + 3
We consider the new divisor 11 and the new remainder 3,and apply the division lemma to get
11 = 3 x 3 + 2
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 416 and 765 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(11,3) = HCF(14,11) = HCF(67,14) = HCF(349,67) = HCF(416,349) = HCF(765,416) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 416, 765 using Euclid's Algorithm
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 416, 765?
Answer: HCF of 416, 765 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 416, 765 using Euclid's Algorithm?
Answer: For arbitrary numbers 416, 765 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.