Highest Common Factor of 7985, 8225, 74415 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 7985, 8225, 74415 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 7985, 8225, 74415 is 5 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 7985, 8225, 74415 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 7985, 8225, 74415 is 5.
HCF(7985, 8225, 74415) = 5
HCF of 7985, 8225, 74415 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7985, 8225, 74415 is 5.
Highest Common Factor of 7985,8225,74415 is 5
Step 1: Since 8225 > 7985, we apply the division lemma to 8225 and 7985, to get
8225 = 7985 x 1 + 240
Step 2: Since the reminder 7985 ≠ 0, we apply division lemma to 240 and 7985, to get
7985 = 240 x 33 + 65
Step 3: We consider the new divisor 240 and the new remainder 65, and apply the division lemma to get
240 = 65 x 3 + 45
We consider the new divisor 65 and the new remainder 45,and apply the division lemma to get
65 = 45 x 1 + 20
We consider the new divisor 45 and the new remainder 20,and apply the division lemma to get
45 = 20 x 2 + 5
We consider the new divisor 20 and the new remainder 5,and apply the division lemma to get
20 = 5 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 7985 and 8225 is 5
Notice that 5 = HCF(20,5) = HCF(45,20) = HCF(65,45) = HCF(240,65) = HCF(7985,240) = HCF(8225,7985) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 74415 > 5, we apply the division lemma to 74415 and 5, to get
74415 = 5 x 14883 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 5 and 74415 is 5
Notice that 5 = HCF(74415,5) .
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Frequently Asked Questions on HCF of 7985, 8225, 74415 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 7985, 8225, 74415?
Answer: HCF of 7985, 8225, 74415 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7985, 8225, 74415 using Euclid's Algorithm?
Answer: For arbitrary numbers 7985, 8225, 74415 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.