Highest Common Factor of 664, 972, 19 using Euclid's algorithm
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, 972, 19 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 664, 972, 19 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, 972, 19 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, 972, 19 is 1.
HCF(664, 972, 19) = 1
HCF of 664, 972, 19 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 664, 972, 19 is 1.
Highest Common Factor of 664,972,19 is 1
Step 1: Since 972 > 664, we apply the division lemma to 972 and 664, to get
972 = 664 x 1 + 308
Step 2: Since the reminder 664 ≠ 0, we apply division lemma to 308 and 664, to get
664 = 308 x 2 + 48
Step 3: We consider the new divisor 308 and the new remainder 48, and apply the division lemma to get
308 = 48 x 6 + 20
We consider the new divisor 48 and the new remainder 20,and apply the division lemma to get
48 = 20 x 2 + 8
We consider the new divisor 20 and the new remainder 8,and apply the division lemma to get
20 = 8 x 2 + 4
We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 664 and 972 is 4
Notice that 4 = HCF(8,4) = HCF(20,8) = HCF(48,20) = HCF(308,48) = HCF(664,308) = HCF(972,664) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 19 > 4, we apply the division lemma to 19 and 4, to get
19 = 4 x 4 + 3
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 3 and 4, to get
4 = 3 x 1 + 1
Step 3: We consider the new divisor 3 and the new remainder 1, and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 4 and 19 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(19,4) .
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Frequently Asked Questions on HCF of 664, 972, 19 using Euclid's Algorithm
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, 972, 19?
Answer: HCF of 664, 972, 19 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 664, 972, 19 using Euclid's Algorithm?
Answer: For arbitrary numbers 664, 972, 19 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.