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 656, 355, 14, 392 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 656, 355, 14, 392 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 656, 355, 14, 392 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 656, 355, 14, 392 is 1.
HCF(656, 355, 14, 392) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 656, 355, 14, 392 is 1.
Step 1: Since 656 > 355, we apply the division lemma to 656 and 355, to get
656 = 355 x 1 + 301
Step 2: Since the reminder 355 ≠ 0, we apply division lemma to 301 and 355, to get
355 = 301 x 1 + 54
Step 3: We consider the new divisor 301 and the new remainder 54, and apply the division lemma to get
301 = 54 x 5 + 31
We consider the new divisor 54 and the new remainder 31,and apply the division lemma to get
54 = 31 x 1 + 23
We consider the new divisor 31 and the new remainder 23,and apply the division lemma to get
31 = 23 x 1 + 8
We consider the new divisor 23 and the new remainder 8,and apply the division lemma to get
23 = 8 x 2 + 7
We consider the new divisor 8 and the new remainder 7,and apply the division lemma to get
8 = 7 x 1 + 1
We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 656 and 355 is 1
Notice that 1 = HCF(7,1) = HCF(8,7) = HCF(23,8) = HCF(31,23) = HCF(54,31) = HCF(301,54) = HCF(355,301) = HCF(656,355) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 14 > 1, we apply the division lemma to 14 and 1, to get
14 = 1 x 14 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 14 is 1
Notice that 1 = HCF(14,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 392 > 1, we apply the division lemma to 392 and 1, to get
392 = 1 x 392 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 392 is 1
Notice that 1 = HCF(392,1) .
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 656, 355, 14, 392?
Answer: HCF of 656, 355, 14, 392 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 656, 355, 14, 392 using Euclid's Algorithm?
Answer: For arbitrary numbers 656, 355, 14, 392 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.