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 974, 558, 553 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 974, 558, 553 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 974, 558, 553 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 974, 558, 553 is 1.
HCF(974, 558, 553) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 974, 558, 553 is 1.
Step 1: Since 974 > 558, we apply the division lemma to 974 and 558, to get
974 = 558 x 1 + 416
Step 2: Since the reminder 558 ≠ 0, we apply division lemma to 416 and 558, to get
558 = 416 x 1 + 142
Step 3: We consider the new divisor 416 and the new remainder 142, and apply the division lemma to get
416 = 142 x 2 + 132
We consider the new divisor 142 and the new remainder 132,and apply the division lemma to get
142 = 132 x 1 + 10
We consider the new divisor 132 and the new remainder 10,and apply the division lemma to get
132 = 10 x 13 + 2
We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 974 and 558 is 2
Notice that 2 = HCF(10,2) = HCF(132,10) = HCF(142,132) = HCF(416,142) = HCF(558,416) = HCF(974,558) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 553 > 2, we apply the division lemma to 553 and 2, to get
553 = 2 x 276 + 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 553 is 1
Notice that 1 = HCF(2,1) = HCF(553,2) .
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 974, 558, 553?
Answer: HCF of 974, 558, 553 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 974, 558, 553 using Euclid's Algorithm?
Answer: For arbitrary numbers 974, 558, 553 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.