Highest Common Factor of 416, 696, 764 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, 696, 764 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 416, 696, 764 is 4 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, 696, 764 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, 696, 764 is 4.
HCF(416, 696, 764) = 4
HCF of 416, 696, 764 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, 696, 764 is 4.
Highest Common Factor of 416,696,764 is 4
Step 1: Since 696 > 416, we apply the division lemma to 696 and 416, to get
696 = 416 x 1 + 280
Step 2: Since the reminder 416 ≠ 0, we apply division lemma to 280 and 416, to get
416 = 280 x 1 + 136
Step 3: We consider the new divisor 280 and the new remainder 136, and apply the division lemma to get
280 = 136 x 2 + 8
We consider the new divisor 136 and the new remainder 8, and apply the division lemma to get
136 = 8 x 17 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 416 and 696 is 8
Notice that 8 = HCF(136,8) = HCF(280,136) = HCF(416,280) = HCF(696,416) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 764 > 8, we apply the division lemma to 764 and 8, to get
764 = 8 x 95 + 4
Step 2: Since the reminder 8 ≠ 0, we apply division lemma to 4 and 8, to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 8 and 764 is 4
Notice that 4 = HCF(8,4) = HCF(764,8) .
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, 696, 764 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, 696, 764?
Answer: HCF of 416, 696, 764 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 416, 696, 764 using Euclid's Algorithm?
Answer: For arbitrary numbers 416, 696, 764 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.