Highest Common Factor of 851, 704, 714 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 851, 704, 714 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 851, 704, 714 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 851, 704, 714 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 851, 704, 714 is 1.
HCF(851, 704, 714) = 1
HCF of 851, 704, 714 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 851, 704, 714 is 1.
Highest Common Factor of 851,704,714 is 1
Step 1: Since 851 > 704, we apply the division lemma to 851 and 704, to get
851 = 704 x 1 + 147
Step 2: Since the reminder 704 ≠ 0, we apply division lemma to 147 and 704, to get
704 = 147 x 4 + 116
Step 3: We consider the new divisor 147 and the new remainder 116, and apply the division lemma to get
147 = 116 x 1 + 31
We consider the new divisor 116 and the new remainder 31,and apply the division lemma to get
116 = 31 x 3 + 23
We consider the new divisor 31 and the new remainder 23,and apply the division lemma to get
31 = 23 x 1 + 8
We consider the new divisor 23 and the new remainder 8,and apply the division lemma to get
23 = 8 x 2 + 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 851 and 704 is 1
Notice that 1 = HCF(7,1) = HCF(8,7) = HCF(23,8) = HCF(31,23) = HCF(116,31) = HCF(147,116) = HCF(704,147) = HCF(851,704) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 714 > 1, we apply the division lemma to 714 and 1, to get
714 = 1 x 714 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 714 is 1
Notice that 1 = HCF(714,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 851, 704, 714 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 851, 704, 714?
Answer: HCF of 851, 704, 714 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 851, 704, 714 using Euclid's Algorithm?
Answer: For arbitrary numbers 851, 704, 714 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.