Highest Common Factor of 500, 370 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, 370 i.e. 10 the largest integer that leaves a remainder zero for all numbers.
HCF of 500, 370 is 10 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, 370 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, 370 is 10.
HCF(500, 370) = 10
HCF of 500, 370 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, 370 is 10.
Highest Common Factor of 500,370 is 10
Step 1: Since 500 > 370, we apply the division lemma to 500 and 370, to get
500 = 370 x 1 + 130
Step 2: Since the reminder 370 ≠ 0, we apply division lemma to 130 and 370, to get
370 = 130 x 2 + 110
Step 3: We consider the new divisor 130 and the new remainder 110, and apply the division lemma to get
130 = 110 x 1 + 20
We consider the new divisor 110 and the new remainder 20,and apply the division lemma to get
110 = 20 x 5 + 10
We consider the new divisor 20 and the new remainder 10,and apply the division lemma to get
20 = 10 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 500 and 370 is 10
Notice that 10 = HCF(20,10) = HCF(110,20) = HCF(130,110) = HCF(370,130) = HCF(500,370) .
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Frequently Asked Questions on HCF of 500, 370 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, 370?
Answer: HCF of 500, 370 is 10 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 500, 370 using Euclid's Algorithm?
Answer: For arbitrary numbers 500, 370 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.