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 655, 8993, 3767 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 655, 8993, 3767 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 655, 8993, 3767 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 655, 8993, 3767 is 1.
HCF(655, 8993, 3767) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 655, 8993, 3767 is 1.
Step 1: Since 8993 > 655, we apply the division lemma to 8993 and 655, to get
8993 = 655 x 13 + 478
Step 2: Since the reminder 655 ≠ 0, we apply division lemma to 478 and 655, to get
655 = 478 x 1 + 177
Step 3: We consider the new divisor 478 and the new remainder 177, and apply the division lemma to get
478 = 177 x 2 + 124
We consider the new divisor 177 and the new remainder 124,and apply the division lemma to get
177 = 124 x 1 + 53
We consider the new divisor 124 and the new remainder 53,and apply the division lemma to get
124 = 53 x 2 + 18
We consider the new divisor 53 and the new remainder 18,and apply the division lemma to get
53 = 18 x 2 + 17
We consider the new divisor 18 and the new remainder 17,and apply the division lemma to get
18 = 17 x 1 + 1
We consider the new divisor 17 and the new remainder 1,and apply the division lemma to get
17 = 1 x 17 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 655 and 8993 is 1
Notice that 1 = HCF(17,1) = HCF(18,17) = HCF(53,18) = HCF(124,53) = HCF(177,124) = HCF(478,177) = HCF(655,478) = HCF(8993,655) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 3767 > 1, we apply the division lemma to 3767 and 1, to get
3767 = 1 x 3767 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 3767 is 1
Notice that 1 = HCF(3767,1) .
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 655, 8993, 3767?
Answer: HCF of 655, 8993, 3767 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 655, 8993, 3767 using Euclid's Algorithm?
Answer: For arbitrary numbers 655, 8993, 3767 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.