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 2142, 8501 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 2142, 8501 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 2142, 8501 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 2142, 8501 is 1.
HCF(2142, 8501) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2142, 8501 is 1.
Step 1: Since 8501 > 2142, we apply the division lemma to 8501 and 2142, to get
8501 = 2142 x 3 + 2075
Step 2: Since the reminder 2142 ≠ 0, we apply division lemma to 2075 and 2142, to get
2142 = 2075 x 1 + 67
Step 3: We consider the new divisor 2075 and the new remainder 67, and apply the division lemma to get
2075 = 67 x 30 + 65
We consider the new divisor 67 and the new remainder 65,and apply the division lemma to get
67 = 65 x 1 + 2
We consider the new divisor 65 and the new remainder 2,and apply the division lemma to get
65 = 2 x 32 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2142 and 8501 is 1
Notice that 1 = HCF(2,1) = HCF(65,2) = HCF(67,65) = HCF(2075,67) = HCF(2142,2075) = HCF(8501,2142) .
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 2142, 8501?
Answer: HCF of 2142, 8501 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2142, 8501 using Euclid's Algorithm?
Answer: For arbitrary numbers 2142, 8501 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.