Highest Common Factor of 748, 1782 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, 1782 i.e. 22 the largest integer that leaves a remainder zero for all numbers.
HCF of 748, 1782 is 22 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, 1782 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, 1782 is 22.
HCF(748, 1782) = 22
HCF of 748, 1782 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, 1782 is 22.
Highest Common Factor of 748,1782 is 22
Step 1: Since 1782 > 748, we apply the division lemma to 1782 and 748, to get
1782 = 748 x 2 + 286
Step 2: Since the reminder 748 ≠ 0, we apply division lemma to 286 and 748, to get
748 = 286 x 2 + 176
Step 3: We consider the new divisor 286 and the new remainder 176, and apply the division lemma to get
286 = 176 x 1 + 110
We consider the new divisor 176 and the new remainder 110,and apply the division lemma to get
176 = 110 x 1 + 66
We consider the new divisor 110 and the new remainder 66,and apply the division lemma to get
110 = 66 x 1 + 44
We consider the new divisor 66 and the new remainder 44,and apply the division lemma to get
66 = 44 x 1 + 22
We consider the new divisor 44 and the new remainder 22,and apply the division lemma to get
44 = 22 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 22, the HCF of 748 and 1782 is 22
Notice that 22 = HCF(44,22) = HCF(66,44) = HCF(110,66) = HCF(176,110) = HCF(286,176) = HCF(748,286) = HCF(1782,748) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 748, 1782 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, 1782?
Answer: HCF of 748, 1782 is 22 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 748, 1782 using Euclid's Algorithm?
Answer: For arbitrary numbers 748, 1782 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.