Highest Common Factor of 746, 460, 270 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 746, 460, 270 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 746, 460, 270 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 746, 460, 270 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 746, 460, 270 is 2.
HCF(746, 460, 270) = 2
HCF of 746, 460, 270 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 746, 460, 270 is 2.
Highest Common Factor of 746,460,270 is 2
Step 1: Since 746 > 460, we apply the division lemma to 746 and 460, to get
746 = 460 x 1 + 286
Step 2: Since the reminder 460 ≠ 0, we apply division lemma to 286 and 460, to get
460 = 286 x 1 + 174
Step 3: We consider the new divisor 286 and the new remainder 174, and apply the division lemma to get
286 = 174 x 1 + 112
We consider the new divisor 174 and the new remainder 112,and apply the division lemma to get
174 = 112 x 1 + 62
We consider the new divisor 112 and the new remainder 62,and apply the division lemma to get
112 = 62 x 1 + 50
We consider the new divisor 62 and the new remainder 50,and apply the division lemma to get
62 = 50 x 1 + 12
We consider the new divisor 50 and the new remainder 12,and apply the division lemma to get
50 = 12 x 4 + 2
We consider the new divisor 12 and the new remainder 2,and apply the division lemma to get
12 = 2 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 746 and 460 is 2
Notice that 2 = HCF(12,2) = HCF(50,12) = HCF(62,50) = HCF(112,62) = HCF(174,112) = HCF(286,174) = HCF(460,286) = HCF(746,460) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 270 > 2, we apply the division lemma to 270 and 2, to get
270 = 2 x 135 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 270 is 2
Notice that 2 = HCF(270,2) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 746, 460, 270 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 746, 460, 270?
Answer: HCF of 746, 460, 270 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 746, 460, 270 using Euclid's Algorithm?
Answer: For arbitrary numbers 746, 460, 270 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.