Highest Common Factor of 500, 372 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, 372 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 500, 372 is 4 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, 372 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, 372 is 4.
HCF(500, 372) = 4
HCF of 500, 372 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, 372 is 4.
Highest Common Factor of 500,372 is 4
Step 1: Since 500 > 372, we apply the division lemma to 500 and 372, to get
500 = 372 x 1 + 128
Step 2: Since the reminder 372 ≠ 0, we apply division lemma to 128 and 372, to get
372 = 128 x 2 + 116
Step 3: We consider the new divisor 128 and the new remainder 116, and apply the division lemma to get
128 = 116 x 1 + 12
We consider the new divisor 116 and the new remainder 12,and apply the division lemma to get
116 = 12 x 9 + 8
We consider the new divisor 12 and the new remainder 8,and apply the division lemma to get
12 = 8 x 1 + 4
We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 500 and 372 is 4
Notice that 4 = HCF(8,4) = HCF(12,8) = HCF(116,12) = HCF(128,116) = HCF(372,128) = HCF(500,372) .
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Frequently Asked Questions on HCF of 500, 372 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, 372?
Answer: HCF of 500, 372 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 500, 372 using Euclid's Algorithm?
Answer: For arbitrary numbers 500, 372 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.