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 557, 502, 756, 78 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 557, 502, 756, 78 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 557, 502, 756, 78 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 557, 502, 756, 78 is 1.
HCF(557, 502, 756, 78) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 557, 502, 756, 78 is 1.
Step 1: Since 557 > 502, we apply the division lemma to 557 and 502, to get
557 = 502 x 1 + 55
Step 2: Since the reminder 502 ≠ 0, we apply division lemma to 55 and 502, to get
502 = 55 x 9 + 7
Step 3: We consider the new divisor 55 and the new remainder 7, and apply the division lemma to get
55 = 7 x 7 + 6
We consider the new divisor 7 and the new remainder 6,and apply the division lemma to get
7 = 6 x 1 + 1
We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 557 and 502 is 1
Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(55,7) = HCF(502,55) = HCF(557,502) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 756 > 1, we apply the division lemma to 756 and 1, to get
756 = 1 x 756 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 756 is 1
Notice that 1 = HCF(756,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 78 > 1, we apply the division lemma to 78 and 1, to get
78 = 1 x 78 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 78 is 1
Notice that 1 = HCF(78,1) .
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 557, 502, 756, 78?
Answer: HCF of 557, 502, 756, 78 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 557, 502, 756, 78 using Euclid's Algorithm?
Answer: For arbitrary numbers 557, 502, 756, 78 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.