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 3615, 8961, 70194 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 3615, 8961, 70194 is 3 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 3615, 8961, 70194 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 3615, 8961, 70194 is 3.
HCF(3615, 8961, 70194) = 3
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 3615, 8961, 70194 is 3.
Step 1: Since 8961 > 3615, we apply the division lemma to 8961 and 3615, to get
8961 = 3615 x 2 + 1731
Step 2: Since the reminder 3615 ≠ 0, we apply division lemma to 1731 and 3615, to get
3615 = 1731 x 2 + 153
Step 3: We consider the new divisor 1731 and the new remainder 153, and apply the division lemma to get
1731 = 153 x 11 + 48
We consider the new divisor 153 and the new remainder 48,and apply the division lemma to get
153 = 48 x 3 + 9
We consider the new divisor 48 and the new remainder 9,and apply the division lemma to get
48 = 9 x 5 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3615 and 8961 is 3
Notice that 3 = HCF(9,3) = HCF(48,9) = HCF(153,48) = HCF(1731,153) = HCF(3615,1731) = HCF(8961,3615) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 70194 > 3, we apply the division lemma to 70194 and 3, to get
70194 = 3 x 23398 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 70194 is 3
Notice that 3 = HCF(70194,3) .
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 3615, 8961, 70194?
Answer: HCF of 3615, 8961, 70194 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 3615, 8961, 70194 using Euclid's Algorithm?
Answer: For arbitrary numbers 3615, 8961, 70194 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.