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 660, 145, 567, 751 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 660, 145, 567, 751 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 660, 145, 567, 751 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 660, 145, 567, 751 is 1.
HCF(660, 145, 567, 751) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 660, 145, 567, 751 is 1.
Step 1: Since 660 > 145, we apply the division lemma to 660 and 145, to get
660 = 145 x 4 + 80
Step 2: Since the reminder 145 ≠ 0, we apply division lemma to 80 and 145, to get
145 = 80 x 1 + 65
Step 3: We consider the new divisor 80 and the new remainder 65, and apply the division lemma to get
80 = 65 x 1 + 15
We consider the new divisor 65 and the new remainder 15,and apply the division lemma to get
65 = 15 x 4 + 5
We consider the new divisor 15 and the new remainder 5,and apply the division lemma to get
15 = 5 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 660 and 145 is 5
Notice that 5 = HCF(15,5) = HCF(65,15) = HCF(80,65) = HCF(145,80) = HCF(660,145) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 567 > 5, we apply the division lemma to 567 and 5, to get
567 = 5 x 113 + 2
Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 2 and 5, to get
5 = 2 x 2 + 1
Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5 and 567 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(567,5) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 751 > 1, we apply the division lemma to 751 and 1, to get
751 = 1 x 751 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 751 is 1
Notice that 1 = HCF(751,1) .
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 660, 145, 567, 751?
Answer: HCF of 660, 145, 567, 751 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 660, 145, 567, 751 using Euclid's Algorithm?
Answer: For arbitrary numbers 660, 145, 567, 751 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.