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 542, 314, 356, 313 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 542, 314, 356, 313 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 542, 314, 356, 313 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 542, 314, 356, 313 is 1.
HCF(542, 314, 356, 313) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 542, 314, 356, 313 is 1.
Step 1: Since 542 > 314, we apply the division lemma to 542 and 314, to get
542 = 314 x 1 + 228
Step 2: Since the reminder 314 ≠ 0, we apply division lemma to 228 and 314, to get
314 = 228 x 1 + 86
Step 3: We consider the new divisor 228 and the new remainder 86, and apply the division lemma to get
228 = 86 x 2 + 56
We consider the new divisor 86 and the new remainder 56,and apply the division lemma to get
86 = 56 x 1 + 30
We consider the new divisor 56 and the new remainder 30,and apply the division lemma to get
56 = 30 x 1 + 26
We consider the new divisor 30 and the new remainder 26,and apply the division lemma to get
30 = 26 x 1 + 4
We consider the new divisor 26 and the new remainder 4,and apply the division lemma to get
26 = 4 x 6 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 542 and 314 is 2
Notice that 2 = HCF(4,2) = HCF(26,4) = HCF(30,26) = HCF(56,30) = HCF(86,56) = HCF(228,86) = HCF(314,228) = HCF(542,314) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 356 > 2, we apply the division lemma to 356 and 2, to get
356 = 2 x 178 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 356 is 2
Notice that 2 = HCF(356,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 313 > 2, we apply the division lemma to 313 and 2, to get
313 = 2 x 156 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 313 is 1
Notice that 1 = HCF(2,1) = HCF(313,2) .
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 542, 314, 356, 313?
Answer: HCF of 542, 314, 356, 313 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 542, 314, 356, 313 using Euclid's Algorithm?
Answer: For arbitrary numbers 542, 314, 356, 313 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.