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 700, 443, 913 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 700, 443, 913 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 700, 443, 913 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 700, 443, 913 is 1.
HCF(700, 443, 913) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 700, 443, 913 is 1.
Step 1: Since 700 > 443, we apply the division lemma to 700 and 443, to get
700 = 443 x 1 + 257
Step 2: Since the reminder 443 ≠ 0, we apply division lemma to 257 and 443, to get
443 = 257 x 1 + 186
Step 3: We consider the new divisor 257 and the new remainder 186, and apply the division lemma to get
257 = 186 x 1 + 71
We consider the new divisor 186 and the new remainder 71,and apply the division lemma to get
186 = 71 x 2 + 44
We consider the new divisor 71 and the new remainder 44,and apply the division lemma to get
71 = 44 x 1 + 27
We consider the new divisor 44 and the new remainder 27,and apply the division lemma to get
44 = 27 x 1 + 17
We consider the new divisor 27 and the new remainder 17,and apply the division lemma to get
27 = 17 x 1 + 10
We consider the new divisor 17 and the new remainder 10,and apply the division lemma to get
17 = 10 x 1 + 7
We consider the new divisor 10 and the new remainder 7,and apply the division lemma to get
10 = 7 x 1 + 3
We consider the new divisor 7 and the new remainder 3,and apply the division lemma to get
7 = 3 x 2 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 700 and 443 is 1
Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(10,7) = HCF(17,10) = HCF(27,17) = HCF(44,27) = HCF(71,44) = HCF(186,71) = HCF(257,186) = HCF(443,257) = HCF(700,443) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 913 > 1, we apply the division lemma to 913 and 1, to get
913 = 1 x 913 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 913 is 1
Notice that 1 = HCF(913,1) .
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 700, 443, 913?
Answer: HCF of 700, 443, 913 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 700, 443, 913 using Euclid's Algorithm?
Answer: For arbitrary numbers 700, 443, 913 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.