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 556, 974 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 556, 974 is 2 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 556, 974 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 556, 974 is 2.
HCF(556, 974) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 556, 974 is 2.
Step 1: Since 974 > 556, we apply the division lemma to 974 and 556, to get
974 = 556 x 1 + 418
Step 2: Since the reminder 556 ≠ 0, we apply division lemma to 418 and 556, to get
556 = 418 x 1 + 138
Step 3: We consider the new divisor 418 and the new remainder 138, and apply the division lemma to get
418 = 138 x 3 + 4
We consider the new divisor 138 and the new remainder 4,and apply the division lemma to get
138 = 4 x 34 + 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 556 and 974 is 2
Notice that 2 = HCF(4,2) = HCF(138,4) = HCF(418,138) = HCF(556,418) = HCF(974,556) .
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 556, 974?
Answer: HCF of 556, 974 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 556, 974 using Euclid's Algorithm?
Answer: For arbitrary numbers 556, 974 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.