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, 969, 413 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 656, 969, 413 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, 969, 413 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, 969, 413 is 1.
HCF(656, 969, 413) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 656, 969, 413 is 1.
Step 1: Since 969 > 656, we apply the division lemma to 969 and 656, to get
969 = 656 x 1 + 313
Step 2: Since the reminder 656 ≠ 0, we apply division lemma to 313 and 656, to get
656 = 313 x 2 + 30
Step 3: We consider the new divisor 313 and the new remainder 30, and apply the division lemma to get
313 = 30 x 10 + 13
We consider the new divisor 30 and the new remainder 13,and apply the division lemma to get
30 = 13 x 2 + 4
We consider the new divisor 13 and the new remainder 4,and apply the division lemma to get
13 = 4 x 3 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 656 and 969 is 1
Notice that 1 = HCF(4,1) = HCF(13,4) = HCF(30,13) = HCF(313,30) = HCF(656,313) = HCF(969,656) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 413 > 1, we apply the division lemma to 413 and 1, to get
413 = 1 x 413 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 413 is 1
Notice that 1 = HCF(413,1) .
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, 969, 413?
Answer: HCF of 656, 969, 413 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 656, 969, 413 using Euclid's Algorithm?
Answer: For arbitrary numbers 656, 969, 413 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.