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 70, 45, 66, 290 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 70, 45, 66, 290 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 70, 45, 66, 290 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 70, 45, 66, 290 is 1.
HCF(70, 45, 66, 290) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 70, 45, 66, 290 is 1.
Step 1: Since 70 > 45, we apply the division lemma to 70 and 45, to get
70 = 45 x 1 + 25
Step 2: Since the reminder 45 ≠ 0, we apply division lemma to 25 and 45, to get
45 = 25 x 1 + 20
Step 3: We consider the new divisor 25 and the new remainder 20, and apply the division lemma to get
25 = 20 x 1 + 5
We consider the new divisor 20 and the new remainder 5, and apply the division lemma to get
20 = 5 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 70 and 45 is 5
Notice that 5 = HCF(20,5) = HCF(25,20) = HCF(45,25) = HCF(70,45) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 66 > 5, we apply the division lemma to 66 and 5, to get
66 = 5 x 13 + 1
Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 1 and 5, to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5 and 66 is 1
Notice that 1 = HCF(5,1) = HCF(66,5) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 290 > 1, we apply the division lemma to 290 and 1, to get
290 = 1 x 290 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 290 is 1
Notice that 1 = HCF(290,1) .
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 70, 45, 66, 290?
Answer: HCF of 70, 45, 66, 290 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 70, 45, 66, 290 using Euclid's Algorithm?
Answer: For arbitrary numbers 70, 45, 66, 290 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.