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 656, 4005, 1223 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 656, 4005, 1223 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 656, 4005, 1223 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 656, 4005, 1223 is 1.
HCF(656, 4005, 1223) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 656, 4005, 1223 is 1.
Step 1: Since 4005 > 656, we apply the division lemma to 4005 and 656, to get
4005 = 656 x 6 + 69
Step 2: Since the reminder 656 ≠ 0, we apply division lemma to 69 and 656, to get
656 = 69 x 9 + 35
Step 3: We consider the new divisor 69 and the new remainder 35, and apply the division lemma to get
69 = 35 x 1 + 34
We consider the new divisor 35 and the new remainder 34,and apply the division lemma to get
35 = 34 x 1 + 1
We consider the new divisor 34 and the new remainder 1,and apply the division lemma to get
34 = 1 x 34 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 656 and 4005 is 1
Notice that 1 = HCF(34,1) = HCF(35,34) = HCF(69,35) = HCF(656,69) = HCF(4005,656) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 1223 > 1, we apply the division lemma to 1223 and 1, to get
1223 = 1 x 1223 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 1223 is 1
Notice that 1 = HCF(1223,1) .
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 656, 4005, 1223?
Answer: HCF of 656, 4005, 1223 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 656, 4005, 1223 using Euclid's Algorithm?
Answer: For arbitrary numbers 656, 4005, 1223 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.