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 718, 977, 402 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 718, 977, 402 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 718, 977, 402 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 718, 977, 402 is 1.
HCF(718, 977, 402) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 718, 977, 402 is 1.
Step 1: Since 977 > 718, we apply the division lemma to 977 and 718, to get
977 = 718 x 1 + 259
Step 2: Since the reminder 718 ≠ 0, we apply division lemma to 259 and 718, to get
718 = 259 x 2 + 200
Step 3: We consider the new divisor 259 and the new remainder 200, and apply the division lemma to get
259 = 200 x 1 + 59
We consider the new divisor 200 and the new remainder 59,and apply the division lemma to get
200 = 59 x 3 + 23
We consider the new divisor 59 and the new remainder 23,and apply the division lemma to get
59 = 23 x 2 + 13
We consider the new divisor 23 and the new remainder 13,and apply the division lemma to get
23 = 13 x 1 + 10
We consider the new divisor 13 and the new remainder 10,and apply the division lemma to get
13 = 10 x 1 + 3
We consider the new divisor 10 and the new remainder 3,and apply the division lemma to get
10 = 3 x 3 + 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 718 and 977 is 1
Notice that 1 = HCF(3,1) = HCF(10,3) = HCF(13,10) = HCF(23,13) = HCF(59,23) = HCF(200,59) = HCF(259,200) = HCF(718,259) = HCF(977,718) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 402 > 1, we apply the division lemma to 402 and 1, to get
402 = 1 x 402 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 402 is 1
Notice that 1 = HCF(402,1) .
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 718, 977, 402?
Answer: HCF of 718, 977, 402 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 718, 977, 402 using Euclid's Algorithm?
Answer: For arbitrary numbers 718, 977, 402 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.