Highest Common Factor of 678, 416 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 678, 416 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 678, 416 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, 416 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, 416 is 2.
HCF(678, 416) = 2
HCF of 678, 416 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 678, 416 is 2.
Highest Common Factor of 678,416 is 2
Step 1: Since 678 > 416, we apply the division lemma to 678 and 416, to get
678 = 416 x 1 + 262
Step 2: Since the reminder 416 ≠ 0, we apply division lemma to 262 and 416, to get
416 = 262 x 1 + 154
Step 3: We consider the new divisor 262 and the new remainder 154, and apply the division lemma to get
262 = 154 x 1 + 108
We consider the new divisor 154 and the new remainder 108,and apply the division lemma to get
154 = 108 x 1 + 46
We consider the new divisor 108 and the new remainder 46,and apply the division lemma to get
108 = 46 x 2 + 16
We consider the new divisor 46 and the new remainder 16,and apply the division lemma to get
46 = 16 x 2 + 14
We consider the new divisor 16 and the new remainder 14,and apply the division lemma to get
16 = 14 x 1 + 2
We consider the new divisor 14 and the new remainder 2,and apply the division lemma to get
14 = 2 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 678 and 416 is 2
Notice that 2 = HCF(14,2) = HCF(16,14) = HCF(46,16) = HCF(108,46) = HCF(154,108) = HCF(262,154) = HCF(416,262) = HCF(678,416) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 678, 416 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 678, 416?
Answer: HCF of 678, 416 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 678, 416 using Euclid's Algorithm?
Answer: For arbitrary numbers 678, 416 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.