Highest Common Factor of 740, 30, 373, 678 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 740, 30, 373, 678 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 740, 30, 373, 678 is 1 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 740, 30, 373, 678 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 740, 30, 373, 678 is 1.
HCF(740, 30, 373, 678) = 1
HCF of 740, 30, 373, 678 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 740, 30, 373, 678 is 1.
Highest Common Factor of 740,30,373,678 is 1
Step 1: Since 740 > 30, we apply the division lemma to 740 and 30, to get
740 = 30 x 24 + 20
Step 2: Since the reminder 30 ≠ 0, we apply division lemma to 20 and 30, to get
30 = 20 x 1 + 10
Step 3: We consider the new divisor 20 and the new remainder 10, and apply the division lemma to get
20 = 10 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 740 and 30 is 10
Notice that 10 = HCF(20,10) = HCF(30,20) = HCF(740,30) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 373 > 10, we apply the division lemma to 373 and 10, to get
373 = 10 x 37 + 3
Step 2: Since the reminder 10 ≠ 0, we apply division lemma to 3 and 10, to get
10 = 3 x 3 + 1
Step 3: We consider the new divisor 3 and the new remainder 1, and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 10 and 373 is 1
Notice that 1 = HCF(3,1) = HCF(10,3) = HCF(373,10) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 678 > 1, we apply the division lemma to 678 and 1, to get
678 = 1 x 678 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 678 is 1
Notice that 1 = HCF(678,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 740, 30, 373, 678 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 740, 30, 373, 678?
Answer: HCF of 740, 30, 373, 678 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 740, 30, 373, 678 using Euclid's Algorithm?
Answer: For arbitrary numbers 740, 30, 373, 678 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.