Highest Common Factor of 500, 778 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 500, 778 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 500, 778 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 500, 778 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, 778 is 2.
HCF(500, 778) = 2
HCF of 500, 778 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 500, 778 is 2.
Highest Common Factor of 500,778 is 2
Step 1: Since 778 > 500, we apply the division lemma to 778 and 500, to get
778 = 500 x 1 + 278
Step 2: Since the reminder 500 ≠ 0, we apply division lemma to 278 and 500, to get
500 = 278 x 1 + 222
Step 3: We consider the new divisor 278 and the new remainder 222, and apply the division lemma to get
278 = 222 x 1 + 56
We consider the new divisor 222 and the new remainder 56,and apply the division lemma to get
222 = 56 x 3 + 54
We consider the new divisor 56 and the new remainder 54,and apply the division lemma to get
56 = 54 x 1 + 2
We consider the new divisor 54 and the new remainder 2,and apply the division lemma to get
54 = 2 x 27 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 500 and 778 is 2
Notice that 2 = HCF(54,2) = HCF(56,54) = HCF(222,56) = HCF(278,222) = HCF(500,278) = HCF(778,500) .
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Frequently Asked Questions on HCF of 500, 778 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 500, 778?
Answer: HCF of 500, 778 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 500, 778 using Euclid's Algorithm?
Answer: For arbitrary numbers 500, 778 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.