Highest Common Factor of 748, 102, 766 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, 102, 766 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 748, 102, 766 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 748, 102, 766 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, 102, 766 is 2.
HCF(748, 102, 766) = 2
HCF of 748, 102, 766 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, 102, 766 is 2.
Highest Common Factor of 748,102,766 is 2
Step 1: Since 748 > 102, we apply the division lemma to 748 and 102, to get
748 = 102 x 7 + 34
Step 2: Since the reminder 102 ≠ 0, we apply division lemma to 34 and 102, to get
102 = 34 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 34, the HCF of 748 and 102 is 34
Notice that 34 = HCF(102,34) = HCF(748,102) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 766 > 34, we apply the division lemma to 766 and 34, to get
766 = 34 x 22 + 18
Step 2: Since the reminder 34 ≠ 0, we apply division lemma to 18 and 34, to get
34 = 18 x 1 + 16
Step 3: We consider the new divisor 18 and the new remainder 16, and apply the division lemma to get
18 = 16 x 1 + 2
We consider the new divisor 16 and the new remainder 2, and apply the division lemma to get
16 = 2 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 34 and 766 is 2
Notice that 2 = HCF(16,2) = HCF(18,16) = HCF(34,18) = HCF(766,34) .
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Frequently Asked Questions on HCF of 748, 102, 766 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, 102, 766?
Answer: HCF of 748, 102, 766 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 748, 102, 766 using Euclid's Algorithm?
Answer: For arbitrary numbers 748, 102, 766 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.