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 3145, 8602 i.e. 17 the largest integer that leaves a remainder zero for all numbers.
HCF of 3145, 8602 is 17 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 3145, 8602 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 3145, 8602 is 17.
HCF(3145, 8602) = 17
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 3145, 8602 is 17.
Step 1: Since 8602 > 3145, we apply the division lemma to 8602 and 3145, to get
8602 = 3145 x 2 + 2312
Step 2: Since the reminder 3145 ≠ 0, we apply division lemma to 2312 and 3145, to get
3145 = 2312 x 1 + 833
Step 3: We consider the new divisor 2312 and the new remainder 833, and apply the division lemma to get
2312 = 833 x 2 + 646
We consider the new divisor 833 and the new remainder 646,and apply the division lemma to get
833 = 646 x 1 + 187
We consider the new divisor 646 and the new remainder 187,and apply the division lemma to get
646 = 187 x 3 + 85
We consider the new divisor 187 and the new remainder 85,and apply the division lemma to get
187 = 85 x 2 + 17
We consider the new divisor 85 and the new remainder 17,and apply the division lemma to get
85 = 17 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 17, the HCF of 3145 and 8602 is 17
Notice that 17 = HCF(85,17) = HCF(187,85) = HCF(646,187) = HCF(833,646) = HCF(2312,833) = HCF(3145,2312) = HCF(8602,3145) .
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 3145, 8602?
Answer: HCF of 3145, 8602 is 17 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 3145, 8602 using Euclid's Algorithm?
Answer: For arbitrary numbers 3145, 8602 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.