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 837, 915 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 837, 915 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 837, 915 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 837, 915 is 3.
HCF(837, 915) = 3
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 837, 915 is 3.
Step 1: Since 915 > 837, we apply the division lemma to 915 and 837, to get
915 = 837 x 1 + 78
Step 2: Since the reminder 837 ≠ 0, we apply division lemma to 78 and 837, to get
837 = 78 x 10 + 57
Step 3: We consider the new divisor 78 and the new remainder 57, and apply the division lemma to get
78 = 57 x 1 + 21
We consider the new divisor 57 and the new remainder 21,and apply the division lemma to get
57 = 21 x 2 + 15
We consider the new divisor 21 and the new remainder 15,and apply the division lemma to get
21 = 15 x 1 + 6
We consider the new divisor 15 and the new remainder 6,and apply the division lemma to get
15 = 6 x 2 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 837 and 915 is 3
Notice that 3 = HCF(6,3) = HCF(15,6) = HCF(21,15) = HCF(57,21) = HCF(78,57) = HCF(837,78) = HCF(915,837) .
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 837, 915?
Answer: HCF of 837, 915 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 837, 915 using Euclid's Algorithm?
Answer: For arbitrary numbers 837, 915 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.