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 664, 975, 36, 219 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 664, 975, 36, 219 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 664, 975, 36, 219 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 664, 975, 36, 219 is 1.
HCF(664, 975, 36, 219) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 664, 975, 36, 219 is 1.
Step 1: Since 975 > 664, we apply the division lemma to 975 and 664, to get
975 = 664 x 1 + 311
Step 2: Since the reminder 664 ≠ 0, we apply division lemma to 311 and 664, to get
664 = 311 x 2 + 42
Step 3: We consider the new divisor 311 and the new remainder 42, and apply the division lemma to get
311 = 42 x 7 + 17
We consider the new divisor 42 and the new remainder 17,and apply the division lemma to get
42 = 17 x 2 + 8
We consider the new divisor 17 and the new remainder 8,and apply the division lemma to get
17 = 8 x 2 + 1
We consider the new divisor 8 and the new remainder 1,and apply the division lemma to get
8 = 1 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 664 and 975 is 1
Notice that 1 = HCF(8,1) = HCF(17,8) = HCF(42,17) = HCF(311,42) = HCF(664,311) = HCF(975,664) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 36 > 1, we apply the division lemma to 36 and 1, to get
36 = 1 x 36 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 36 is 1
Notice that 1 = HCF(36,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 219 > 1, we apply the division lemma to 219 and 1, to get
219 = 1 x 219 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 219 is 1
Notice that 1 = HCF(219,1) .
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 664, 975, 36, 219?
Answer: HCF of 664, 975, 36, 219 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 664, 975, 36, 219 using Euclid's Algorithm?
Answer: For arbitrary numbers 664, 975, 36, 219 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.