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, 510, 767 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 716, 510, 767 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, 510, 767 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, 510, 767 is 1.
HCF(716, 510, 767) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 716, 510, 767 is 1.
Step 1: Since 716 > 510, we apply the division lemma to 716 and 510, to get
716 = 510 x 1 + 206
Step 2: Since the reminder 510 ≠ 0, we apply division lemma to 206 and 510, to get
510 = 206 x 2 + 98
Step 3: We consider the new divisor 206 and the new remainder 98, and apply the division lemma to get
206 = 98 x 2 + 10
We consider the new divisor 98 and the new remainder 10,and apply the division lemma to get
98 = 10 x 9 + 8
We consider the new divisor 10 and the new remainder 8,and apply the division lemma to get
10 = 8 x 1 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 716 and 510 is 2
Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(98,10) = HCF(206,98) = HCF(510,206) = HCF(716,510) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 767 > 2, we apply the division lemma to 767 and 2, to get
767 = 2 x 383 + 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 767 is 1
Notice that 1 = HCF(2,1) = HCF(767,2) .
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 716, 510, 767?
Answer: HCF of 716, 510, 767 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 716, 510, 767 using Euclid's Algorithm?
Answer: For arbitrary numbers 716, 510, 767 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.