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 965, 66230 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 965, 66230 is 5 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 965, 66230 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 965, 66230 is 5.
HCF(965, 66230) = 5
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 965, 66230 is 5.
Step 1: Since 66230 > 965, we apply the division lemma to 66230 and 965, to get
66230 = 965 x 68 + 610
Step 2: Since the reminder 965 ≠ 0, we apply division lemma to 610 and 965, to get
965 = 610 x 1 + 355
Step 3: We consider the new divisor 610 and the new remainder 355, and apply the division lemma to get
610 = 355 x 1 + 255
We consider the new divisor 355 and the new remainder 255,and apply the division lemma to get
355 = 255 x 1 + 100
We consider the new divisor 255 and the new remainder 100,and apply the division lemma to get
255 = 100 x 2 + 55
We consider the new divisor 100 and the new remainder 55,and apply the division lemma to get
100 = 55 x 1 + 45
We consider the new divisor 55 and the new remainder 45,and apply the division lemma to get
55 = 45 x 1 + 10
We consider the new divisor 45 and the new remainder 10,and apply the division lemma to get
45 = 10 x 4 + 5
We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get
10 = 5 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 965 and 66230 is 5
Notice that 5 = HCF(10,5) = HCF(45,10) = HCF(55,45) = HCF(100,55) = HCF(255,100) = HCF(355,255) = HCF(610,355) = HCF(965,610) = HCF(66230,965) .
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 965, 66230?
Answer: HCF of 965, 66230 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 965, 66230 using Euclid's Algorithm?
Answer: For arbitrary numbers 965, 66230 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.