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 3605, 9770, 39680 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 3605, 9770, 39680 is 5 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 3605, 9770, 39680 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 3605, 9770, 39680 is 5.
HCF(3605, 9770, 39680) = 5
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 3605, 9770, 39680 is 5.
Step 1: Since 9770 > 3605, we apply the division lemma to 9770 and 3605, to get
9770 = 3605 x 2 + 2560
Step 2: Since the reminder 3605 ≠ 0, we apply division lemma to 2560 and 3605, to get
3605 = 2560 x 1 + 1045
Step 3: We consider the new divisor 2560 and the new remainder 1045, and apply the division lemma to get
2560 = 1045 x 2 + 470
We consider the new divisor 1045 and the new remainder 470,and apply the division lemma to get
1045 = 470 x 2 + 105
We consider the new divisor 470 and the new remainder 105,and apply the division lemma to get
470 = 105 x 4 + 50
We consider the new divisor 105 and the new remainder 50,and apply the division lemma to get
105 = 50 x 2 + 5
We consider the new divisor 50 and the new remainder 5,and apply the division lemma to get
50 = 5 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 3605 and 9770 is 5
Notice that 5 = HCF(50,5) = HCF(105,50) = HCF(470,105) = HCF(1045,470) = HCF(2560,1045) = HCF(3605,2560) = HCF(9770,3605) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 39680 > 5, we apply the division lemma to 39680 and 5, to get
39680 = 5 x 7936 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 5 and 39680 is 5
Notice that 5 = HCF(39680,5) .
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 3605, 9770, 39680?
Answer: HCF of 3605, 9770, 39680 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 3605, 9770, 39680 using Euclid's Algorithm?
Answer: For arbitrary numbers 3605, 9770, 39680 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.