Highest Common Factor of 800, 7544, 7664 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 800, 7544, 7664 i.e. 8 the largest integer that leaves a remainder zero for all numbers.
HCF of 800, 7544, 7664 is 8 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 800, 7544, 7664 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 800, 7544, 7664 is 8.
HCF(800, 7544, 7664) = 8
HCF of 800, 7544, 7664 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 800, 7544, 7664 is 8.
Highest Common Factor of 800,7544,7664 is 8
Step 1: Since 7544 > 800, we apply the division lemma to 7544 and 800, to get
7544 = 800 x 9 + 344
Step 2: Since the reminder 800 ≠ 0, we apply division lemma to 344 and 800, to get
800 = 344 x 2 + 112
Step 3: We consider the new divisor 344 and the new remainder 112, and apply the division lemma to get
344 = 112 x 3 + 8
We consider the new divisor 112 and the new remainder 8, and apply the division lemma to get
112 = 8 x 14 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 800 and 7544 is 8
Notice that 8 = HCF(112,8) = HCF(344,112) = HCF(800,344) = HCF(7544,800) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 7664 > 8, we apply the division lemma to 7664 and 8, to get
7664 = 8 x 958 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 8 and 7664 is 8
Notice that 8 = HCF(7664,8) .
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Frequently Asked Questions on HCF of 800, 7544, 7664 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 800, 7544, 7664?
Answer: HCF of 800, 7544, 7664 is 8 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 800, 7544, 7664 using Euclid's Algorithm?
Answer: For arbitrary numbers 800, 7544, 7664 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.