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, 428 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 664, 428 is 4 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, 428 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, 428 is 4.
HCF(664, 428) = 4
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 664, 428 is 4.
Step 1: Since 664 > 428, we apply the division lemma to 664 and 428, to get
664 = 428 x 1 + 236
Step 2: Since the reminder 428 ≠ 0, we apply division lemma to 236 and 428, to get
428 = 236 x 1 + 192
Step 3: We consider the new divisor 236 and the new remainder 192, and apply the division lemma to get
236 = 192 x 1 + 44
We consider the new divisor 192 and the new remainder 44,and apply the division lemma to get
192 = 44 x 4 + 16
We consider the new divisor 44 and the new remainder 16,and apply the division lemma to get
44 = 16 x 2 + 12
We consider the new divisor 16 and the new remainder 12,and apply the division lemma to get
16 = 12 x 1 + 4
We consider the new divisor 12 and the new remainder 4,and apply the division lemma to get
12 = 4 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 664 and 428 is 4
Notice that 4 = HCF(12,4) = HCF(16,12) = HCF(44,16) = HCF(192,44) = HCF(236,192) = HCF(428,236) = HCF(664,428) .
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, 428?
Answer: HCF of 664, 428 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 664, 428 using Euclid's Algorithm?
Answer: For arbitrary numbers 664, 428 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.