Highest Common Factor of 748, 670 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, 670 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 748, 670 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, 670 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, 670 is 2.
HCF(748, 670) = 2
HCF of 748, 670 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, 670 is 2.
Highest Common Factor of 748,670 is 2
Step 1: Since 748 > 670, we apply the division lemma to 748 and 670, to get
748 = 670 x 1 + 78
Step 2: Since the reminder 670 ≠ 0, we apply division lemma to 78 and 670, to get
670 = 78 x 8 + 46
Step 3: We consider the new divisor 78 and the new remainder 46, and apply the division lemma to get
78 = 46 x 1 + 32
We consider the new divisor 46 and the new remainder 32,and apply the division lemma to get
46 = 32 x 1 + 14
We consider the new divisor 32 and the new remainder 14,and apply the division lemma to get
32 = 14 x 2 + 4
We consider the new divisor 14 and the new remainder 4,and apply the division lemma to get
14 = 4 x 3 + 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 748 and 670 is 2
Notice that 2 = HCF(4,2) = HCF(14,4) = HCF(32,14) = HCF(46,32) = HCF(78,46) = HCF(670,78) = HCF(748,670) .
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, 670 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, 670?
Answer: HCF of 748, 670 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 748, 670 using Euclid's Algorithm?
Answer: For arbitrary numbers 748, 670 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.