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 500, 781 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 500, 781 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 500, 781 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 500, 781 is 1.
HCF(500, 781) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 500, 781 is 1.
Step 1: Since 781 > 500, we apply the division lemma to 781 and 500, to get
781 = 500 x 1 + 281
Step 2: Since the reminder 500 ≠ 0, we apply division lemma to 281 and 500, to get
500 = 281 x 1 + 219
Step 3: We consider the new divisor 281 and the new remainder 219, and apply the division lemma to get
281 = 219 x 1 + 62
We consider the new divisor 219 and the new remainder 62,and apply the division lemma to get
219 = 62 x 3 + 33
We consider the new divisor 62 and the new remainder 33,and apply the division lemma to get
62 = 33 x 1 + 29
We consider the new divisor 33 and the new remainder 29,and apply the division lemma to get
33 = 29 x 1 + 4
We consider the new divisor 29 and the new remainder 4,and apply the division lemma to get
29 = 4 x 7 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 500 and 781 is 1
Notice that 1 = HCF(4,1) = HCF(29,4) = HCF(33,29) = HCF(62,33) = HCF(219,62) = HCF(281,219) = HCF(500,281) = HCF(781,500) .
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 500, 781?
Answer: HCF of 500, 781 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 500, 781 using Euclid's Algorithm?
Answer: For arbitrary numbers 500, 781 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.