Highest Common Factor of 415, 732, 38, 700 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 415, 732, 38, 700 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 415, 732, 38, 700 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 415, 732, 38, 700 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 415, 732, 38, 700 is 1.
HCF(415, 732, 38, 700) = 1
HCF of 415, 732, 38, 700 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 415, 732, 38, 700 is 1.
Highest Common Factor of 415,732,38,700 is 1
Step 1: Since 732 > 415, we apply the division lemma to 732 and 415, to get
732 = 415 x 1 + 317
Step 2: Since the reminder 415 ≠ 0, we apply division lemma to 317 and 415, to get
415 = 317 x 1 + 98
Step 3: We consider the new divisor 317 and the new remainder 98, and apply the division lemma to get
317 = 98 x 3 + 23
We consider the new divisor 98 and the new remainder 23,and apply the division lemma to get
98 = 23 x 4 + 6
We consider the new divisor 23 and the new remainder 6,and apply the division lemma to get
23 = 6 x 3 + 5
We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get
6 = 5 x 1 + 1
We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 415 and 732 is 1
Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(23,6) = HCF(98,23) = HCF(317,98) = HCF(415,317) = HCF(732,415) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 38 > 1, we apply the division lemma to 38 and 1, to get
38 = 1 x 38 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 38 is 1
Notice that 1 = HCF(38,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 700 > 1, we apply the division lemma to 700 and 1, to get
700 = 1 x 700 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 700 is 1
Notice that 1 = HCF(700,1) .
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Frequently Asked Questions on HCF of 415, 732, 38, 700 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 415, 732, 38, 700?
Answer: HCF of 415, 732, 38, 700 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 415, 732, 38, 700 using Euclid's Algorithm?
Answer: For arbitrary numbers 415, 732, 38, 700 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.