Highest Common Factor of 782, 138 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 782, 138 i.e. 46 the largest integer that leaves a remainder zero for all numbers.
HCF of 782, 138 is 46 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 782, 138 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 782, 138 is 46.
HCF(782, 138) = 46
HCF of 782, 138 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 782, 138 is 46.
Highest Common Factor of 782,138 is 46
Step 1: Since 782 > 138, we apply the division lemma to 782 and 138, to get
782 = 138 x 5 + 92
Step 2: Since the reminder 138 ≠ 0, we apply division lemma to 92 and 138, to get
138 = 92 x 1 + 46
Step 3: We consider the new divisor 92 and the new remainder 46, and apply the division lemma to get
92 = 46 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 46, the HCF of 782 and 138 is 46
Notice that 46 = HCF(92,46) = HCF(138,92) = HCF(782,138) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 782, 138 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 782, 138?
Answer: HCF of 782, 138 is 46 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 782, 138 using Euclid's Algorithm?
Answer: For arbitrary numbers 782, 138 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
