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 635, 7732, 7660 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 635, 7732, 7660 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 635, 7732, 7660 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 635, 7732, 7660 is 1.
HCF(635, 7732, 7660) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 635, 7732, 7660 is 1.
Step 1: Since 7732 > 635, we apply the division lemma to 7732 and 635, to get
7732 = 635 x 12 + 112
Step 2: Since the reminder 635 ≠ 0, we apply division lemma to 112 and 635, to get
635 = 112 x 5 + 75
Step 3: We consider the new divisor 112 and the new remainder 75, and apply the division lemma to get
112 = 75 x 1 + 37
We consider the new divisor 75 and the new remainder 37,and apply the division lemma to get
75 = 37 x 2 + 1
We consider the new divisor 37 and the new remainder 1,and apply the division lemma to get
37 = 1 x 37 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 635 and 7732 is 1
Notice that 1 = HCF(37,1) = HCF(75,37) = HCF(112,75) = HCF(635,112) = HCF(7732,635) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 7660 > 1, we apply the division lemma to 7660 and 1, to get
7660 = 1 x 7660 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 7660 is 1
Notice that 1 = HCF(7660,1) .
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 635, 7732, 7660?
Answer: HCF of 635, 7732, 7660 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 635, 7732, 7660 using Euclid's Algorithm?
Answer: For arbitrary numbers 635, 7732, 7660 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.