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 720, 986, 257 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 720, 986, 257 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 720, 986, 257 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 720, 986, 257 is 1.
HCF(720, 986, 257) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 720, 986, 257 is 1.
Step 1: Since 986 > 720, we apply the division lemma to 986 and 720, to get
986 = 720 x 1 + 266
Step 2: Since the reminder 720 ≠ 0, we apply division lemma to 266 and 720, to get
720 = 266 x 2 + 188
Step 3: We consider the new divisor 266 and the new remainder 188, and apply the division lemma to get
266 = 188 x 1 + 78
We consider the new divisor 188 and the new remainder 78,and apply the division lemma to get
188 = 78 x 2 + 32
We consider the new divisor 78 and the new remainder 32,and apply the division lemma to get
78 = 32 x 2 + 14
We consider the new divisor 32 and the new remainder 14,and apply the division lemma to get
32 = 14 x 2 + 4
We consider the new divisor 14 and the new remainder 4,and apply the division lemma to get
14 = 4 x 3 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 720 and 986 is 2
Notice that 2 = HCF(4,2) = HCF(14,4) = HCF(32,14) = HCF(78,32) = HCF(188,78) = HCF(266,188) = HCF(720,266) = HCF(986,720) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 257 > 2, we apply the division lemma to 257 and 2, to get
257 = 2 x 128 + 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 257 is 1
Notice that 1 = HCF(2,1) = HCF(257,2) .
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 720, 986, 257?
Answer: HCF of 720, 986, 257 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 720, 986, 257 using Euclid's Algorithm?
Answer: For arbitrary numbers 720, 986, 257 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.