Highest Common Factor of 748, 7260, 6116 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 748, 7260, 6116 i.e. 44 the largest integer that leaves a remainder zero for all numbers.
HCF of 748, 7260, 6116 is 44 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 748, 7260, 6116 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 748, 7260, 6116 is 44.
HCF(748, 7260, 6116) = 44
HCF of 748, 7260, 6116 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 748, 7260, 6116 is 44.
Highest Common Factor of 748,7260,6116 is 44
Step 1: Since 7260 > 748, we apply the division lemma to 7260 and 748, to get
7260 = 748 x 9 + 528
Step 2: Since the reminder 748 ≠ 0, we apply division lemma to 528 and 748, to get
748 = 528 x 1 + 220
Step 3: We consider the new divisor 528 and the new remainder 220, and apply the division lemma to get
528 = 220 x 2 + 88
We consider the new divisor 220 and the new remainder 88,and apply the division lemma to get
220 = 88 x 2 + 44
We consider the new divisor 88 and the new remainder 44,and apply the division lemma to get
88 = 44 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 44, the HCF of 748 and 7260 is 44
Notice that 44 = HCF(88,44) = HCF(220,88) = HCF(528,220) = HCF(748,528) = HCF(7260,748) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 6116 > 44, we apply the division lemma to 6116 and 44, to get
6116 = 44 x 139 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 44, the HCF of 44 and 6116 is 44
Notice that 44 = HCF(6116,44) .
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Frequently Asked Questions on HCF of 748, 7260, 6116 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 748, 7260, 6116?
Answer: HCF of 748, 7260, 6116 is 44 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 748, 7260, 6116 using Euclid's Algorithm?
Answer: For arbitrary numbers 748, 7260, 6116 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.