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 370, 680, 31 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 370, 680, 31 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 370, 680, 31 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 370, 680, 31 is 1.
HCF(370, 680, 31) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 370, 680, 31 is 1.
Step 1: Since 680 > 370, we apply the division lemma to 680 and 370, to get
680 = 370 x 1 + 310
Step 2: Since the reminder 370 ≠ 0, we apply division lemma to 310 and 370, to get
370 = 310 x 1 + 60
Step 3: We consider the new divisor 310 and the new remainder 60, and apply the division lemma to get
310 = 60 x 5 + 10
We consider the new divisor 60 and the new remainder 10, and apply the division lemma to get
60 = 10 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 370 and 680 is 10
Notice that 10 = HCF(60,10) = HCF(310,60) = HCF(370,310) = HCF(680,370) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 31 > 10, we apply the division lemma to 31 and 10, to get
31 = 10 x 3 + 1
Step 2: Since the reminder 10 ≠ 0, we apply division lemma to 1 and 10, to get
10 = 1 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 10 and 31 is 1
Notice that 1 = HCF(10,1) = HCF(31,10) .
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 370, 680, 31?
Answer: HCF of 370, 680, 31 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 370, 680, 31 using Euclid's Algorithm?
Answer: For arbitrary numbers 370, 680, 31 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.