Highest Common Factor of 716, 417, 496 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 716, 417, 496 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 716, 417, 496 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 716, 417, 496 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 716, 417, 496 is 1.
HCF(716, 417, 496) = 1
HCF of 716, 417, 496 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 716, 417, 496 is 1.
Highest Common Factor of 716,417,496 is 1
Step 1: Since 716 > 417, we apply the division lemma to 716 and 417, to get
716 = 417 x 1 + 299
Step 2: Since the reminder 417 ≠ 0, we apply division lemma to 299 and 417, to get
417 = 299 x 1 + 118
Step 3: We consider the new divisor 299 and the new remainder 118, and apply the division lemma to get
299 = 118 x 2 + 63
We consider the new divisor 118 and the new remainder 63,and apply the division lemma to get
118 = 63 x 1 + 55
We consider the new divisor 63 and the new remainder 55,and apply the division lemma to get
63 = 55 x 1 + 8
We consider the new divisor 55 and the new remainder 8,and apply the division lemma to get
55 = 8 x 6 + 7
We consider the new divisor 8 and the new remainder 7,and apply the division lemma to get
8 = 7 x 1 + 1
We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 716 and 417 is 1
Notice that 1 = HCF(7,1) = HCF(8,7) = HCF(55,8) = HCF(63,55) = HCF(118,63) = HCF(299,118) = HCF(417,299) = HCF(716,417) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 496 > 1, we apply the division lemma to 496 and 1, to get
496 = 1 x 496 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 496 is 1
Notice that 1 = HCF(496,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 716, 417, 496 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 716, 417, 496?
Answer: HCF of 716, 417, 496 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 716, 417, 496 using Euclid's Algorithm?
Answer: For arbitrary numbers 716, 417, 496 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.