Highest Common Factor of 51, 714, 748 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 51, 714, 748 i.e. 17 the largest integer that leaves a remainder zero for all numbers.
HCF of 51, 714, 748 is 17 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 51, 714, 748 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 51, 714, 748 is 17.
HCF(51, 714, 748) = 17
HCF of 51, 714, 748 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 51, 714, 748 is 17.
Highest Common Factor of 51,714,748 is 17
Step 1: Since 714 > 51, we apply the division lemma to 714 and 51, to get
714 = 51 x 14 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 51, the HCF of 51 and 714 is 51
Notice that 51 = HCF(714,51) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 748 > 51, we apply the division lemma to 748 and 51, to get
748 = 51 x 14 + 34
Step 2: Since the reminder 51 ≠ 0, we apply division lemma to 34 and 51, to get
51 = 34 x 1 + 17
Step 3: We consider the new divisor 34 and the new remainder 17, and apply the division lemma to get
34 = 17 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 17, the HCF of 51 and 748 is 17
Notice that 17 = HCF(34,17) = HCF(51,34) = HCF(748,51) .
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Frequently Asked Questions on HCF of 51, 714, 748 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 51, 714, 748?
Answer: HCF of 51, 714, 748 is 17 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 51, 714, 748 using Euclid's Algorithm?
Answer: For arbitrary numbers 51, 714, 748 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.