Highest Common Factor of 910, 8498, 3100 using Euclid's algorithm
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 910, 8498, 3100 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 910, 8498, 3100 is 2 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 910, 8498, 3100 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 910, 8498, 3100 is 2.
HCF(910, 8498, 3100) = 2
HCF of 910, 8498, 3100 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 910, 8498, 3100 is 2.
Highest Common Factor of 910,8498,3100 is 2
Step 1: Since 8498 > 910, we apply the division lemma to 8498 and 910, to get
8498 = 910 x 9 + 308
Step 2: Since the reminder 910 ≠ 0, we apply division lemma to 308 and 910, to get
910 = 308 x 2 + 294
Step 3: We consider the new divisor 308 and the new remainder 294, and apply the division lemma to get
308 = 294 x 1 + 14
We consider the new divisor 294 and the new remainder 14, and apply the division lemma to get
294 = 14 x 21 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 14, the HCF of 910 and 8498 is 14
Notice that 14 = HCF(294,14) = HCF(308,294) = HCF(910,308) = HCF(8498,910) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 3100 > 14, we apply the division lemma to 3100 and 14, to get
3100 = 14 x 221 + 6
Step 2: Since the reminder 14 ≠ 0, we apply division lemma to 6 and 14, to get
14 = 6 x 2 + 2
Step 3: We consider the new divisor 6 and the new remainder 2, and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 14 and 3100 is 2
Notice that 2 = HCF(6,2) = HCF(14,6) = HCF(3100,14) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 910, 8498, 3100 using Euclid's Algorithm
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 910, 8498, 3100?
Answer: HCF of 910, 8498, 3100 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 910, 8498, 3100 using Euclid's Algorithm?
Answer: For arbitrary numbers 910, 8498, 3100 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.