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 470, 330, 277, 39 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 470, 330, 277, 39 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 470, 330, 277, 39 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 470, 330, 277, 39 is 1.
HCF(470, 330, 277, 39) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 470, 330, 277, 39 is 1.
Step 1: Since 470 > 330, we apply the division lemma to 470 and 330, to get
470 = 330 x 1 + 140
Step 2: Since the reminder 330 ≠ 0, we apply division lemma to 140 and 330, to get
330 = 140 x 2 + 50
Step 3: We consider the new divisor 140 and the new remainder 50, and apply the division lemma to get
140 = 50 x 2 + 40
We consider the new divisor 50 and the new remainder 40,and apply the division lemma to get
50 = 40 x 1 + 10
We consider the new divisor 40 and the new remainder 10,and apply the division lemma to get
40 = 10 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 470 and 330 is 10
Notice that 10 = HCF(40,10) = HCF(50,40) = HCF(140,50) = HCF(330,140) = HCF(470,330) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 277 > 10, we apply the division lemma to 277 and 10, to get
277 = 10 x 27 + 7
Step 2: Since the reminder 10 ≠ 0, we apply division lemma to 7 and 10, to get
10 = 7 x 1 + 3
Step 3: We consider the new divisor 7 and the new remainder 3, and apply the division lemma to get
7 = 3 x 2 + 1
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 277 is 1
Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(10,7) = HCF(277,10) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 39 > 1, we apply the division lemma to 39 and 1, to get
39 = 1 x 39 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 39 is 1
Notice that 1 = HCF(39,1) .
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 470, 330, 277, 39?
Answer: HCF of 470, 330, 277, 39 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 470, 330, 277, 39 using Euclid's Algorithm?
Answer: For arbitrary numbers 470, 330, 277, 39 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.