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 678, 1742 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 678, 1742 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 678, 1742 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 678, 1742 is 2.
HCF(678, 1742) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 678, 1742 is 2.
Step 1: Since 1742 > 678, we apply the division lemma to 1742 and 678, to get
1742 = 678 x 2 + 386
Step 2: Since the reminder 678 ≠ 0, we apply division lemma to 386 and 678, to get
678 = 386 x 1 + 292
Step 3: We consider the new divisor 386 and the new remainder 292, and apply the division lemma to get
386 = 292 x 1 + 94
We consider the new divisor 292 and the new remainder 94,and apply the division lemma to get
292 = 94 x 3 + 10
We consider the new divisor 94 and the new remainder 10,and apply the division lemma to get
94 = 10 x 9 + 4
We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get
10 = 4 x 2 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 678 and 1742 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(94,10) = HCF(292,94) = HCF(386,292) = HCF(678,386) = HCF(1742,678) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 678, 1742?
Answer: HCF of 678, 1742 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 678, 1742 using Euclid's Algorithm?
Answer: For arbitrary numbers 678, 1742 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.