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 506, 910 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 506, 910 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 506, 910 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 506, 910 is 2.
HCF(506, 910) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 506, 910 is 2.
Step 1: Since 910 > 506, we apply the division lemma to 910 and 506, to get
910 = 506 x 1 + 404
Step 2: Since the reminder 506 ≠ 0, we apply division lemma to 404 and 506, to get
506 = 404 x 1 + 102
Step 3: We consider the new divisor 404 and the new remainder 102, and apply the division lemma to get
404 = 102 x 3 + 98
We consider the new divisor 102 and the new remainder 98,and apply the division lemma to get
102 = 98 x 1 + 4
We consider the new divisor 98 and the new remainder 4,and apply the division lemma to get
98 = 4 x 24 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 506 and 910 is 2
Notice that 2 = HCF(4,2) = HCF(98,4) = HCF(102,98) = HCF(404,102) = HCF(506,404) = HCF(910,506) .
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 506, 910?
Answer: HCF of 506, 910 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 506, 910 using Euclid's Algorithm?
Answer: For arbitrary numbers 506, 910 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.