Highest Common Factor of 7534, 5224, 66404 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 7534, 5224, 66404 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 7534, 5224, 66404 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 7534, 5224, 66404 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 7534, 5224, 66404 is 2.
HCF(7534, 5224, 66404) = 2
HCF of 7534, 5224, 66404 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7534, 5224, 66404 is 2.
Highest Common Factor of 7534,5224,66404 is 2
Step 1: Since 7534 > 5224, we apply the division lemma to 7534 and 5224, to get
7534 = 5224 x 1 + 2310
Step 2: Since the reminder 5224 ≠ 0, we apply division lemma to 2310 and 5224, to get
5224 = 2310 x 2 + 604
Step 3: We consider the new divisor 2310 and the new remainder 604, and apply the division lemma to get
2310 = 604 x 3 + 498
We consider the new divisor 604 and the new remainder 498,and apply the division lemma to get
604 = 498 x 1 + 106
We consider the new divisor 498 and the new remainder 106,and apply the division lemma to get
498 = 106 x 4 + 74
We consider the new divisor 106 and the new remainder 74,and apply the division lemma to get
106 = 74 x 1 + 32
We consider the new divisor 74 and the new remainder 32,and apply the division lemma to get
74 = 32 x 2 + 10
We consider the new divisor 32 and the new remainder 10,and apply the division lemma to get
32 = 10 x 3 + 2
We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 7534 and 5224 is 2
Notice that 2 = HCF(10,2) = HCF(32,10) = HCF(74,32) = HCF(106,74) = HCF(498,106) = HCF(604,498) = HCF(2310,604) = HCF(5224,2310) = HCF(7534,5224) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 66404 > 2, we apply the division lemma to 66404 and 2, to get
66404 = 2 x 33202 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 66404 is 2
Notice that 2 = HCF(66404,2) .
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Frequently Asked Questions on HCF of 7534, 5224, 66404 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 7534, 5224, 66404?
Answer: HCF of 7534, 5224, 66404 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7534, 5224, 66404 using Euclid's Algorithm?
Answer: For arbitrary numbers 7534, 5224, 66404 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.